(4) Decide which of the following maps f R2 R2 are isometries. Justify your answers. : (v.) f(x,y) = (1-x, 3+ y).

Let A = {4, 5, 7} and B = {x, y}. Let p1 and p2 be the projections of A ✕ B onto the first and second coordinates. That is, for each pair (a, b)  A ✕ B, p1(a, b) = a and p2(a, b) = b. (a) Find p1(4, y) and p1(7, x) What is the range of p1? (Enter your answer in set-roster notation.) (b) Find p2(4, y) and p2(7, x). What is the range of p2? (Enter your answer in set-roster notation.)

Force F in rectangular x-y components is given by F = -25i + 28j [N]. Determine the non- rectangular components of F in the y- and h-directions in N. Enter the y-component. 1 F 30° h

Please help with this!

Describe (in the form y = f(x)) the images of the lines u = 6 and v = 6 under the mapping G(u, v) = (,u? – v). (Express numbers in exact form. Use symbolic notation and fractions where needed.) image of u = 6: y = image of v = 6: y =

5

Prove that the symmetric difference quotient is the average of the slopes of the secant lines from x to x + h and from x - h to x.

Consider the map G(u, v) = (2u + v, 8u + 3v) from the uv-plane to the xy-plane. G maps the line v = mu to a line through the origin in the xy-plane. Find the slope of this line. (Express numbers in exact form. Use symbolic notation and fractions where needed.) slope:

Please find the discriminant

a) Consider the function f (x, y) VIn (4 – x² – y²). Find the domain and range of f(x, y).