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A rocket moves forward with velocity v = 3c/4, with respect to the earth. Inside this rocket, a second, smaller rocket is launched. In the inertial frame of reference where the larger rocket is at rest, the smaller rocket has velocity v = 3c/4. What is the velocity of the smaller rocket with respect to the earth? You may express the answer as a fraction times c, if you wish (but simplify as much as possible).
A sphere of radius R is uniformly charged to a total charge of Q. It is made to spin about an axis that passes through its center with an angular speed ω. Find the magnitude of the resulting magnetic field at the center of the sphere.
A resistor is in the shape of a cube, with each side of resistance R . Find the equivalent resistance between any two of its adjacent corners.
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