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question:Do free-falling objects accelerate at about 10 m/s² due to the forces of friction and air resistance?

answer:False. Free-falling objects accelerate at about 9.8 m/s² due to the force of gravity, not friction or air resistance.

question:How does temperature affect the transition between different states of matter?

answer:Temperature plays a crucial role in the transitions among solid, liquid, and gas states of matter. As a substance undergoes phase changes, its temperature responds accordingly. For instance, consider a block of ice at room temperature. The heat from the surroundings is transferred to the ice. Initially, the temperature of the ice remains constant as this heat energy is used to break the intermolecular bonds holding the water molecules together in a solid structure (this is known as the latent heat of fusion). Once sufficient energy has been absorbed, the ice's molecular bonds break, and the molecules start moving faster, increasing their kinetic energy and thus their temperature. This increase in molecular motion leads to the transition from a solid (ice) to a liquid (water) through the process of melting. Similarly, when a liquid is heated further, its temperature will rise until it reaches the boiling point, where it will then change into a gas (vaporization) without a further increase in temperature, as long as the heat input is used to break the intermolecular forces and not increase the kinetic energy. In summary, temperature affects the states of matter by inducing phase changes, where energy is used to alter the molecular interactions rather than just increasing the kinetic energy.

question:What is the length of the radius of a circle with its center at the origin (0, 0), given that the point (5, -12) lies on the circle?

answer:The radius of the circle is the distance between its center and any point on the circle. Since the center is at the origin (0, 0), and one point on the circle is (5, -12), we can use the distance formula to find the radius. The distance formula for two points (x1, y1) and (x2, y2) is: [ sqrt{(x2 - x1)^2 + (y2 - y1)^2} ] In this case, (x1, y1) = (0, 0) and (x2, y2) = (5, -12). Plugging in the values: [ sqrt{(5 - 0)^2 + (-12 - 0)^2} = sqrt{25 + 144} = sqrt{169} ] The radius is thus 13 units, which can also be derived from recognizing that this forms a right triangle with sides 5 and 12, and the radius is the hypotenuse of this triangle.

question:Find the value of x-y where x=frac{2}{3}+frac{7 i}{3} and y=-frac{23}{3}+frac{4 i}{3}.

answer:To find x-y, we can subtract the corresponding real and imaginary parts of x and y. Real parts: frac{2}{3} - (-frac{23}{3}) = frac{2}{3} + frac{23}{3} = frac{25}{3} Imaginary parts: frac{7 i}{3} - frac{4 i}{3} = frac{3 i}{3} = i Therefore, x-y = frac{25}{3} + i. The answer is frac{25}{3}+i

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