2. We say that two matrices A and B commute if A B = B A. Matrices do not commute in general, but certain types of matrices do. Which of the following types of matrices commute? Assume matrices are 4 x 4. • scaling matrices S,S2 • translation matrices TT2 • rotation matrices, R,R2 • rotation and translation, RT • scaling and translation, ST scaling and rotation, SR To prove each one formally, you would need to write out a general form of each type of matrix and do the brute force calculation which wouldn't help you much in terms of how to think about it. Instead, try to visualize it. For cases of failure imagine a counterexample. 3. There are two ways to define a 3D dot product of two vectors u and v, namely the sum of U;V; for i = 1, ..3, and | u || v | cos(0). In lecture 2, I sketched out an argument for why these definitions are equivalent. Write out the same sketch for the 3D case.

The number of insects attracted to bright light is currently 8. If the number is expected to quadruple every 9 minutes, how long will it take for the number to reach 900?

Jean typically takes 2 less hours than Donald to assemble a bicycle if each works alone. Jean and Donald worked together to assemble a bicycle for 1 hour, and then Donald finished the job without Jean after an additional 1 hour. How long would it have taken Donald to assemble the bicycle alone? Do not include the units in your answer.

A person invested $7,400 in an account growing at a rate allowing the money to double every 6 years. How much money would be in the account after 4 years, to the nearest dollar?