Let V and W be vector spaces, and let T W V ! W be a linear transformation. Given a subspace U of V , let T .U / denote the set of all images of the form T .x/, where x is in U. Show that T .U / is a subspace of W .

In a heat engine if 1000 j of heat enters the system the piston does 500 j of work, what is the final internal energy of the system if the initial energy was 2000 j? 1. write the equation 2.list out your known variables 3.plug the numbers into the equations 4.solve 5.write your solution statement that includes initial energy and final

Astone weighing 1.5 kilograms is resting on a rock at a height of 20 meters above the ground. the stone rolls down 10 meters and comes to rest on a patch of moss. the gravitational potential energy of the stone on the moss is joules.

Which radioisotope is used in dating geological formations?