Denote the mass and the radius of the earth by m and r. a satellite of mass m is circulating around the earth at a radius of r = 4r . r r r = 4r find the energy required to launch the satellite from the earth into its orbit. make use of conservation of energy

Tafari worked one summer on a ship that set weather buoys in the ocean. he watched how one of the buoys moved in the water. describe which parts of the wave would cause the buoy to bob up and down. which wave property determined how fast the buoys bobbed in the water? he observed that when the wind blew harder, the ocean waves were larger, and the buoys moved away from the ship. what effect, if any, did the waves have on how far the buoys moved? explain your answer.

Write the equation for momentum, first using symbols for the variables, then using words for the variables.

Let v1, v2, w be three linearly independent vectors in r 3 . that is, they do not all lie on the same plane. for each of the following (infinite) set of vectors, carefully sketch it in r 3 , and determine whether or not it is a vector space (i.e., a subspace of r 3 ). explain your reasoning