7.1

1. I hate to be not helpful, but I had Math 190 last semester, so groups are pretty fresh in my mind. No problems here.

2. I get the impression that transformations are associated a lot with groups. If one were designing/creating a computer program that had an interface that mimicked that natural, tangible, physical interface we have, I bet it would be useful to be able to prove that any transformation was the composition of perhaps simpler transformations, proving that transformations were closed under composition and that any manipulation the user might make could be predicted, or at least its result could be. This is probably a very rudimentary application, if it even is one.