For any string w = w1w2 · · · wn, the reverse of w, written w R, is the string w in reverse order, wn · · · w2w1. For any language A, let A R = {w R| w ∈ A}. Show that if A is regular, so is A R.

Acave rescue team lifts an injured spelunker directly upward and out of a sinkhole by means of a motor-driven cable. the lift is performed in three stages, each requiring a vertical distance of 10.0 m: (a) the initially stationary spelunker is accelerated to a speed of 4.90 m/s; (b) he is then lifted at the constant speed of 4.90 m/s; (c) finally he is decelerated to zero speed. how much work is done on the 68.0 kg rescue by the force lifting him during each stage?