Let q be an m x m orthogonal matrix. (a) prove that for any given vectors u and v in rm, the angle between u and v is the same as the angle between qu and qv. (b) prove that |q|2 = 1. (c) give an example 2 x 2 orthogonal matrix q, such that ||q||1 #1 and ||q|00 1 (d) prove that |qa|| = || ||2, for any mx m matrix a.

A) if $50000 is invested in a bank account that pays 9.3% of interest compounded on a six-monthly basis, how much money will be in the account after 3 and 12 years? b) if matusalen's father had put $2.0 in the bank when he was born and there, how long would matusalen have had to his death (969 years later) if the interest was 7% per year composed each month and weekly?

What values of x satisfy the inequality x^2-9x< 0? how is your answer shown on the graph?

Mike wants to make meatloaf. his recipe uses a total of 8 pounds of meat. if he uses a 3 to 1 ratio of beef to pork, how much pork will he use? enter your answer as a mixed number in simplest terms.