Write Scheme functions to do the following. You are only allowed to use the functions introduced in our lecture notes and the helper functions written by yourself. (a) Return all rotations of a given list. For example, (rotate ’(a b c d e)) should return ((a b c d e) (b c d e a) (c d e a b) (d e a b c) (e a b c d)) (in some order). (b) Return a list containing all elements of a given list that satisfy a given predicate. For example, (filter (lambda (x) (< x 5)) ’(3 9 5 8 2 4 7)) should return (3 2 4).