if a is a matrix with columns that span rn, then ax = b has a solution for all b in rn.

The statement that is true about electromagnets is that these magnet work only when electric current passed through them.

Electromagnets are called temporary magnets because they do not show magnetic properties all the time.

They only show the magnetic properties when the current is passing through them.

As soon as the current in the Electromagnet stops they stops behaving like a magnet.

This property of temporary magnetism of the Electromagnet allows the Electromagnet to be used in devices like magnetic locks, MRI machines, headphones and loudspeakers.

Material like Copper, nickel and Cobalt are used to create electromagnets.

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A doubling current through an inductor causes the energy stored there to vary by a factor of four. There is no expectation that an inductor will lose energy.

Only when necessary does it supply energy to the circuit from its storage. The voltage across the inductor will gradually change if the current is passed through it. In the 1800s, Oersted demonstrated how a conductor carrying current generates a magnetic field all around it. The movement of electrical charge carriers like electrons is known as current. Positive and negative locations both experience current flow. The ampere is the SI unit for calculating electrical current (A). A passive two-terminal electrical component known as an inductor, also known as a coil, choke, or reactor, stores energy in a magnetic field as electric current passes through it.

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A frame of reference should be created to characterize the situation. To determine the position of objects, we often use the earth as a reference point.

A frame of reference should be created to characterize the situation. To determine the position of objects, we often use the earth as a reference point. It is important to remember that in this situation you should almost always use a moving reference rather than a static one.

View objects as if they were on a number line to understand their position in a straight line. Any position along the number line is allowed for both positive and negative numbers. It is common to place the initial position of the object at the zero mark.

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The correct option is (a) i.e. a galaxy in the local group, galaxies is likely to be oldest.

A galaxy is a collection of stars, stellar remains, interstellar gas, dust, and dark matter that are gravitationally bonded together. The name comes from the Greek word galaxias, which means "milky" and refers to the Milky Way galaxy, which houses the Solar System. Galaxies, which contain an average of 100 million stars, range in size from dwarfs, which contain fewer than 100 million stars, to supergiants, which contain 100 trillion stars, all of which orbit the galaxy's center of mass. Only a small percentage of the mass in a normal galaxy is visible in the form of stars and nebulae; the majority of the galaxy's mass is dark matter. Supermassive black holes are a typical component of galaxy centers. According on their optical shape, galaxies are classified as elliptical, spiral, or irregular. It is believed that the nuclei of many of them contain supermassive black holes. Sagittarius A*, the name of the Milky Way's primary black hole, is four million times more massive than the Sun. GN-z11 is the oldest and furthest away galaxy as of March 2016. It can be seen as having existed only 400 million years after the Big Bang and is located 32 billion light-years away from Earth.

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Answer:

Below

Explanation:

40 w  * 2 hr/day  * 30 day = 2400 w - hr =  2.4 kw hr

Calculated energy consumed by the television is 2.4 kW-hr. when Television set of 40 watt is used for 2 hours per day for 30 days.

Power is the rate of doing work. Power is also defined as work divided by time. i.e. Power = Work ÷ Time. Its  SI unit is Watt denoted by letter W. Watt(W) means J/s or J.s-1. Something makes work in less time, it means it has more power. Work is Force times Displacement.

Dimension of Power is [M¹ L² T⁻³]

Given,

Power P = 40W = 0.04 kW

Time = 2 hr × 30 days = 60 hr

Energy in kW-hr =?

By using formula,

P = Energy ÷ Time

Energy E = Power × Time

E = P× t

E = 0.04 kW × 60 hr

E = 2.4 kW-hr.

Hence energy consumed by television is 2.4 kW-hr.

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The work done on the car by this force will be 11000 J

The work will be shown in the region under the F-x graph. The definition of work is the dot product of the force applied to an item and the displacement caused by that force.

The vertical axis of a force-displacement graph will contain force (in N) and the horizontal axis will have displacement (in m).

The graph's area is equal to F.s.

This amount also indicates the labour put into making the thing.

The overall displacement is represented by the area under the velocity/time curve.

The average velocity is obtained by dividing it by the change in time.

Speed is expressed vectorially as velocity.

The area of the F-x graph is the work

[tex]w=(22 \times 200)+\left(\frac{1}{2} \times 22 \times 3 \times 200\right)[/tex]

w=4400+6600

w=11000 J

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The complete question should be:

A car is pushed along a long road that is straight, horizontal, and parallel to the x direction. The horizontal force on the car varies with x as shown in the figure. What is the work done on the car by this force? (Let a = 200 N.) J

There were 585 gm of nacl (mm = 58.5 g/mol) in the 100 µl of PBS solution.

As per the details given in the above question are as bellow,

The details are as follow,

100 µl contained the mass of Nacl (mm=58.5 g/mol).

Nacl=0.1mM  [tex]\left(1 \mathrm{mM}=10^{-3} \mathrm{M}\right)[/tex]

Solving further we get,

[tex]& \Rightarrow 0.1 \times 10^{-3} M=0.1 \times 10^{-3} \frac{\mathrm{mol}}{\mathrm{L}}[/tex]

Now taking the volume,

Volume taken = 100 μL. [tex]\quad\left(1_\mu=10^{-6}\right)[/tex]

[tex]& \Rightarrow 100 \times 10^{-6} \mathrm{~L}=10^{-4} \mathrm{~L} \text {. }[/tex]

Molarity into Volume is the definition of a mole.

[tex]=0.1 \times 10^{-3} \frac{\mathrm{mol}}{\mathrm{L}} \times 10^{-4} \mathrm{~L} \\[/tex]

Further we get,

[tex]& =0.1 \times 10^{-7} \mathrm{~mol} \\[/tex]

We get the mole is,

mole =58.5 g/mol

[tex]& \Rightarrow 0.1 \times 10^{-7} \mathrm{~mol}=58.5 \frac{\mathrm{g}}{\mathrm{m}=1} \times 0.1 \times 10^{-7} \mathrm{m.1}[/tex]

Solving further we get,

[tex]& =0.585 \times 10^{-6} \mathrm{gm}=585 \times 10^{-9} \mathrm{gm} .[/tex]

=585gm

Molarity

A solute's concentration in a solution, specifically the quantity of it per unit volume of solution, is measured by its molar concentration, which is a chemical word. The number of moles per litre, denoted by the unit sign mol/L, is the molarity unit that is most frequently used in chemistry.

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It will take the boat an infinite amount of time to cross the river, as it is not moving relative to the water.

To determine the time required for the crossing, you can use the formula:

In this case, the distance is 1 km and the speed is the speed of the boat relative to the water. Since the speed of the water in the river is 5 km per hour and the boat is capable of a maximum speed of 5 km per hour in still water, the speed of the boat relative to the water is zero.

Therefore, the time required for the crossing is:

This means that it will take the boat an infinite amount of time to cross the river, as it is not moving relative to the water. To make the crossing, the boat will need to have a speed greater than zero relative to the water. This can be achieved by either increasing the speed of the boat or by decreasing the speed of the water relative to the boat, for example by rowing against the current.

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Answer:

boiling point

Explanation:

In the case of boiling point, the presence of solute particles in a solution causes the boiling point of the solution to be higher than that of the pure solvent. This is because the solute particles interfere with the movement of the solvent molecules, making it more difficult for them to escape from the surface of the solution and enter the gas phase.

If Bi < 1, it means that there are very few temperature variations inside the solid. These conditions may the lumped capacitance method be used to predict the transient response of a solid to a change in its thermal environment

Under what condition is the lumped capacitance method valid?

A lumped capacitance study is often regarded as legitimate if the Biot number of the heat transfer scenario is less than 0.1.

What is the necessary condition that must be satisfied in order to apply the lumped system analysis?

The conduction heat resistance is negligible because lumped system analysis assumes a homogeneous temperature distribution throughout the body. As a result, when Bi = 0, the lumped system analysis is accurate. For lumped system analysis, tiny bodies with high heat conductivity make for suitable candidates.

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The required force exerted on the master cylinder of a hydraulic lift to support the weight of a 2500-kg car is 147 Newton.

The hydraulic pressure on both cylinders are the same.

F₁ / A₁ = F₂ / A₂

Where:

F₁  = force on master cylinder

F₂ = force on slave cylinder

A₁ = cross section area of master cylinder

A₂ = cross section area of slave cylinder

In the given problem, the force acted on the slave cylinder is equal to the weight of the car. Hence,

F₂ = 2500 x 9.8 = 24,500 N

A₁ = 1/4 x 3.14 x 1.93² = 2.92 cm²

A₂ = 1/4 x 3.14 x 24.9² = 486.7 cm²

Plug these parameters into the equation:

F₁ / 2.92 = 24,500 / 486.7

F₁ = (24,500 / 486.7) x 2.92 = 147 Newton

Hence, the required force is 147 Newton

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Even among atoms of the same element, the number of neutrons might vary. Atoms of the same element that have different numbers of neutrons but the same number of protons are called isotopes.

The only difference between identical chemical element atoms of various isotopes is the amount of neutrons in the nucleus.

Isotopes are variations in the mass number, "A," of an element's atoms that share the same number of protons (atomic number, "Z") but a different number of neutrons. Consider hydrogen as an example. It has the isotopes 1H, 2H, and 3H in its naturally occurring form.

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The rate of turn can be increased and the radius of turn decreased by decreasing airspeed and shallowing the bank. Option C.

Turn radius depends on both airspeed and bank angle. The turning radius at any bank angle is directly proportional to the airspeed squared. Doubling the airspeed quadruples the turning radius, and trebling the airspeed quadruples the radius.

During a constant banked turn, increasing airspeed will decrease turn speed and increase turn radius. Airplanes fly fast, but the distance they fly is faster than their speed. As a result, it takes longer to complete a turn and slows down the turn.

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According to the question if the force acts on the bullet for 0.1 sec the final velocity of the bullet is 800 m/s.

In science, the term "force" has a particular definition. At this point, describing a force as pushing or pulling is quite acceptable. In the notion of a force, there both are living organisms and inanimate objects.

F = m x a

Solving for a,

a = F/m

Substituting the known values,

a = (200 N)/(0.025 kg) = 8000 m/s²

The maximum velocity of the bullet is the product of the acceleration and the given time.

v = (8000 m/s²)(0.1 s) = 800 m/s

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A basic simple harmonic oscillator completes 5 full vibrations in 12.0 seconds. Its motion has a period of 2.40 seconds, a frequency of 0.417 Hz, and an angular frequency of 2.62 rad/s.

We may calculate the period and, thus, the frequency by measuring the length of one full oscillation. The motion's frequency, f = 1/T = /2, determines how many complete oscillations occur in a given amount of time.

(a)Given that time taken for an oscillator to undergo 5 complete vibrations (t) = 12s

Period = time taken/total number of vibrations(T) = 12/5 = 2.40s

(b) frequency is inversely proportional to time. So f = 1/T

f = 1/2.40 = 0.417Hz

(c) the angular frequency is calculated as  ω=2πf

ω=2x(3.14)x0.417 = 2.62 rad/s

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The difference in temperature between the fahrenheit and kelvin scales is 574.25 degrees, while the difference between the fahrenheit and celsius scales is -40 degrees Celsius.

(a) Given that F = C, the relationship between the fahrenheit and celsius scales is

°F = (°C * 9/5) + 32

°F -32 = (°F * 9/5)

°F = -40

(b)  the relationship between the fahrenheit and kelvin scales is (F - 32 )/9 = (K - 273 )/5,

Let F = K

(F - 32 )/9 = (F - 273 )/5 = 574.25

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The spring constant of the spring to which a block is attached and the spring is compressed initially and then released is 16.67 N/m.

According to Hooke's Law,

When a spring is stretched, the force applied is proportional to the lengthening from the equilibrium length.

The formula k = -F/x, where k is the spring constant, can be used to get the spring constant. F stands for force, and x is for the variation in spring length.

As per the Law of Conservation of Energy

Energy follows the principle of conservation when it is moved from one form to another.

So, initial energy = final energy

=> 1/2 * k * x² = 1/2 * m * v²

where k is the spring constant

Compression of the spring = 0.75 m

m = Mass of the block = 1.5 kg

v = velocity of the block = 2.5 m/s

So, from the above expression

1/2* k * (0.75)² = 1/2* (1.5)* (2.5)²

k * (0.75)² = (1.5)* (2.5)²

k = [(1.5)* (2.5)²]/(0.75)² = 9.375/0.5625 = 16.67 N/m

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Heat energy amount 0.99J which refrigerator deliver to the reservoir at 320K.

We know that for refrigerator we need to find the cooling factor. For cooling factor we know that cooling factor is find by the ratio of temperature at different times. Heat energy is released by the refrigerator for making cooling factor as maximum as possible.

Using the formula of cooling factor, we get

=>β = T₂/T₁ -1

where T₂ is temperature after refrigerator lose heat

and T₁ is temperature before lose heat

415=T₂/270 -1

=>415+1 = T₂/270

=>416=T₂/270

=>T₂=416 ˣ 270

=>T₂=112320

Now, we need to find the energy at temperature 320K and at T₂.

So, Heat Energy=1 - 320/112320

=> Heat Energy=(112320-320)/112320

=>Heat Energy=112000/112320

=>Heat Energy=0.99J

Hence, heat energy deliver to the reservoir is 0.99J

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The area of the portion of the plane is 10x+7y+z=4. It is contained within the 15π√150 elliptic cylinder.

A cylinder has a volume of r2 h and a surface area of r2 h + r2 h.

We are given;

10x + 7y + z = 4

Making z the subject, we have;

z = 4 - 10x - 7y

area of the surface as part of z = f(x, y) is;

A(S) = ∫∫√[(∂f/∂x)² + (∂f/∂y)² + 1]dA

z = 4 - 10x - 7y,

∂f/∂x = -10

∂f/∂y = -7

Thus;

A(S) = ∫∫√[(-10)² + (-7)² + 1]dA

A(S) = √150 ∫∫dA

Where ∫∫dA is the elliptical cylinder

Using the formula for the general form of an elliptical area,

x²/a² + y²/b² = 1 and comparing with

x²/25 + y²/9 = 1, we have;

a = 5 and b = 3

So, area of elliptical cylinder = πab

Thus;

A(S) = √150 × π(5 × 3)

A(S) = 15π√150

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Acceleration is equal to velocity (meter/sec)/time (sec). Therefore, (meter/sec)/sec = (meter/sec)/sec is the unit of acceleration. 1200N.

If the elevator is stationary or traveling at a constant speed, N = mg. If the elevator accelerates upward, N = mg + ma. If the elevator has a downward acceleration, N = mg - ma. The perceived weight of the person is greater than the actual weight if the elevator is ascending quickly. if the elevator is descending more quickly.

Acceleration on a ramp is equal to the product of gravitational acceleration and the height-to-length ratio of the ramp. Acceleration on a ramp is equal to gravity acceleration times the sine of the ramp angle.

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The potential difference across each light bulb would always be the same as the potential difference across the battery cells.

Potential difference is described as the amount of work energy required to move an electric charge from one point to another and can also be the difference in electric potential between two points.

Two light bulbs in a simple parallel circuit each will enjoy the full voltage of the battery. Hence, the reason why the bulbs in the parallel circuit will be brighter than those in the series circuit.

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b. -2.5 [tex]ms^{-2}[/tex] is the magnitude of the acceleration of the boat when it travels 12 m.

We can find the acceleration using ,

[tex]v^{2} -u^{2} = 2as[/tex],

Where,

v ⇒final velocity,

u ⇒initial velocity,

a ⇒acceleration,

s ⇒distance covered.

Initial velocity(u)= 9.5 [tex]ms^{-1}[/tex]

final velocity (v)= 5.5 [tex]ms^{-1}[/tex]

Distance (s) = 12 m

Putting the values we get,

[tex]v^{2} -u^{2} = 2as[/tex]

a =[tex]\frac{v^{2} -u^{2}}{2s}[/tex]

a= [tex]\frac{(5.5)^{2} -(9.5)^{2}}{(2)(12)}[/tex]

a=[tex]\frac{30.25 -90.25}{(24)}[/tex]

a=[tex]\frac{-60}{2000}[/tex]

a= -2.5

(It is negative acceleration since it has a negative sign. )

Hence, the magnitude of the acceleration of the boat is  -2.5 [tex]ms^{-2}[/tex]

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Camping - Even on sweltering summer days, camping is a delightful outdoor activity.

However, if it's hot outside, your tent may become very uncomfortable. Thankfully, there are ways to keep your tent cool. By making the most of your supplies, setting up your tent in the ideal location, and using a tarp or umbrella to block off the sun, you may avoid the heat.

Three methods to keep the tent cool:

1. Bring your cooler of ice into the tent.

2. Use a battery-operated fan to circulate the air.

3. Open your tent’s door and vents if it has any.

4. Sleep on top of your sleeping bag to stay cool.

5. Remove the rain fly if the weather forecast doesn’t predict rain.

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1.35µm is the width of single slit that produces its first minimum for 633-nm light at an angle of 28.0º.

Light encounters a number of phenomena while traveling through air, including interference, refraction, reflection, and diffraction. Diffraction of light happens when light strikes an obstruction.

When light passes through a single slit whose width (w) is on the order of the light's wavelength, we can witness single slit diffraction. The screen's diffraction pattern will be located L >> w distant from the slit. The tilt affects the intensity.

As we known that

  D sinx= mλ

where

D is width of single slit

x is angle of diffraction

λ is the wavelength of the light

m is the order of diffraction

After put all the values in above equation we get

D sin 28° =(633 *[tex]10^{-9}[/tex] m)

D =1.35µm

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Answer:

P. E = mgh

when g= 10ms^-1

1000j = 5 × 10 × h

1000j = 50h

h = 1000 ÷ 50

h = 2Om

The direction and amount of force the water exerts on it is equivalent to the weight of the can up.

A floating object moves a weight of fluid equal to its own weight when it displaces a weight of water equal to its own weight. According to Archimedes' principle, the buoyant force and the fluid displacement's weight are equivalent.

The upthrust in the water matches the weight of the body in the water it floats, where upthrust is the upward vertical force applied on an item in fluid.

Hence the buoyancy principle is used when the can is floating below the lake's surface. Water will be pushing upward with a force equal to the weight of the can.

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Thermal efficiency if the gas volume is halved during the adiabatic compression n=24%

Any thermal cycle's efficiency is expressed as:

                                    [tex]n=1-\frac{Tc}{Th}------(1)[/tex]

We know that for an adiabatic process:

[tex]p^{v^{Y} }=const[/tex]

From the first law, we may express pressure in terms of temperature.

[tex]p^{v} =nRT\\\\p=\frac{nRT}{v} \alpha Tv^{-1}[/tex]

As a result, we have the following for an adiabatic process:

[tex]Tv^{Y-1} =const[/tex]

Step: 2 Equating:

Let us now calculate a temperature ratio based on the volume ratio:

[tex]TcVc^{Y-1} =ThVh^{y-1}[/tex]

We get that:

[tex]\frac{Tc}{Th} =\frac{Vh^{Y-1} } {Vc^{Y-1} } =(\frac{Vh}{Vc} )^{Y-1}[/tex]

Finding the value of Efficiency:

The Efficiency will be,

[tex]n=1-(\frac{Vh}{Vc}) ^{Y-1} \\\\n=1-(\frac{1}{2} )^{1.40-1}[/tex]

n=24%

∴The thermal efficiency n=24%

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Upon calculation the value of centripetal force in this question is found to be 3399.79 N

The value of coefficient of friction is calculated to be 0.231.

This question can be solved using the concepts of friction and circular motion.

a) Centripetal force is the force acting on an object traveling in a circle that is directed inward toward the center of the circle. Centrifugal force is the force that acts in the opposing direction and points away from the point of rotation. The centrifugal and centripetal forces acting on a rotating body have equal magnitude but opposing directions.

Time period T=[tex]\frac{2\pi r}{v}[/tex]

v= velocity of object

r= radius of circular path

which means [tex]v=\frac{2\pi r}{T}[/tex]

On putting the values r=4, T=8.34 and solving

v=3.011 m/s

Now as we know the centripetal force is given by [tex]\frac{mv^{2} }{r}[/tex]

[tex]F_{c} =\frac{mv^{2} }{r}[/tex]

m= mass of the object

v= velocity of the object

r= radius of the circular path

Putting v= 3.011m/s, r=4m, m=1500 kg in the formula for centripetal force

we get [tex]F_{c} =3399.79 N\\[/tex]

b) Coefficient of friction-The coefficient of friction, which is equal to the ratio between the maximum frictional force that the surface exerts and the force pushing the object toward the surface, is a measurement of the degree of frictional force that a surface exerts on any substances moving over it. It depends on the material of the object.

The formula for coefficient of friction for circular motion is given by:

μ=[tex]\frac{v^{2} }{rg}[/tex]

μ= coefficient of friction

r= radius of circular path

g= acceleration due to gravity

v= velocity of object

Putting v= 3.011 m/s , r=4meter, g= 9.8ms⁻² and solving

The value of coefficient of friction can be calculated to be 0.231

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The calculated answer is 2 m/s. The displacement that an object or particle experiences with respect to time is expressed vectorially as velocity.

The energy that drives motion is known as kinetic energy (KE). Kinetic energy is the force that drives motion. The mass and speed of an object moving determine how much kinetic energy it has. The formula for calculating it is

KE = 1 2 mass velocity 2.

The relationship between kinetic energy and an object's mass and square of its velocity is direct:

K.E. = 1/2 m v2.

The kinetic energy is measured in kilograms-meters squared per second squared if the mass is measured in kilograms and the velocity is measured in meters per second.

4= 1*v²

=2 m/s

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The second law of thermodynamics states that the universe's entropy always rises for all spontaneous reactions (positive).

negative

The reaction will be spontaneous at low temperatures if -T-S is positive and -H is negative (decreasing the magnitude of the entropy term). The reaction will be spontaneous at high temperatures if H is positive and T is negative (increasing the magnitude of the entropy term).

Any process that happens spontaneously under specific circumstances and in a specific direction is said to as spontaneous. Without outside assistance, each choice develops on its own.

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