) Let (x, y) €RXR. Consider the following functions from R2 to R? r((x, y) = (-y, x) and s(x, y) = (x, -y). (a) What is the order of r? of s? Justify. Note: r" = rororo...or. n times (b) Let f be of...

Extracted text: ) Let (x, y) €RXR. Consider the following functions from R2 to R? r((x, y) = (-y, x) and s(x, y) = (x, -y). (a) What is the order of r? of s? Justify. Note: r" = rororo...or. n times (b) Let f be of the form r's' where 0 s i s Irl and 0 sjs Isl. Fill in the table with these distinct function and their images. image of (x, y) f (x, y) i (-у. х) (x,-y) It may be nice to enumerate the elements alphabetically, e.g. list rs ahead of r's. (c) Draw the point P(x, y) on quadrant I of the real plane. Show the image of P under each function f excer for the identity i. (d) The set K = {r's | 0sis r| and 0sis Isl} is a group. Construct the complete group table for K. 1 P(x, y) 1 of 2