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A pilot flying from Honolulu to California flies at an airspeed of 300.0 m/s ("airspeed" - airplane's speed through the surrounding air) with her airplane pointed 67.0 degrees to the east of north. However, the air itself is moving with a 75.0-m/s windspeed blowing due east. When the pilot adds together the two vectors of her airspeed and the windspeed, she gets her groundspeed: the airplane's actual velocity relative to the ground below. (Even though these are called "speeds" by pilots, they are all vector velocities.) Using either the component method of the "triangle" method, find the magnitude and compass bearing (expressed in degrees to the east of north) of the airplane's groundspeed.
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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