) Let (x, y) €Rx R. 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 is Ir| and 0 sjs Isl. Fill in the table with these distinct funct and their images. image of (x, y) f i (x, y) (-y, x) (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 ex for the identity i. (d) The set K = {rs' | 0sis Ir| and osjs Isl } is a group. Construct the complete group table for K

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