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Air traffic controllers use radar to keep track of the location of aircraft. The radar displays an aircraft's location in terms of the compass direction from the controller to the aircraft, and the horizontal distance along the ground between the two. In addition, the aircraft transmits its altitude to the controller automatically. Create a coordinate system by making east the positive x axis, north the positive y axis, and altitude the z axis. An aircraft is approaching at an altitude of 5.0 km, a horizontal distance of 35 km, and a bearing of 65° east of north. Write its position vector in rectangular coordinates.
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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