The collection Mn of n-by-n matrices is a vector space in the usual way: You can add matrices component-wise and multiply all their entries by scalars. Really, it is just a repackaging of R n 2 . Consider the linear map S : Mn → Mn given by S(A) = (A−At )/2, where t is the transpose. (a) (2 points) Apply S to a 2-by-2 matrix of your choice (don’t pick a trivial matrix, like the identity or the zero matrix).

Shryia read a 481 -page-long book cover to cover in a single session, at a constant rate. after reading for 1.5 hours, she had 403 pages left to read. how fast was shryia reading? pages per hour how long did it take her to read the entire book? hours plz i realy need this

Driving 75 mph, it takes alicia 2 hours to reach the airport to go on a vacation. it then takes her 4 hours to get to her destination with the jet traveling at a speed of 400 mph. how many miles does alicia travel to get to her destination?

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?