Problem 1 Convert the following vectors from Cartesian (x, } to polar (r, 6) or polar to Cartesian coordinates. Give all answers to 2 signicant gures. All angles should be between 0 and 360. a) (m) = (4:6): r = , 9 = b) (m) = (-5. -1): r = ,9 = c) ($36) = (7. 165): x = ,y = d) (r, 9) = (2, 250): x = ,y = Problem 2 John walks from his home due east for 1 mile, due north-east for 3 miles, due west for 2 miles, and then walks straight home. a) Write down the Cartesian coordinates of the vector that takes him home. x = miles, y = miles b) What was the distance that John traveled in miles? miles c) What was John's displacement in miles? miles d) If the excursion lasted a total of 3 hours, what was John's average speed in miles per hour (mph)? mph e) What was John's average velocity in mph? mph