Let (u, v) = (u 2 , v). Is one-to-one? If not, determine a domain on which is one-to-one. Find the image under

Let Φ(u, v) = (u², v). Is Φ one-to-one? If not, determine a domain on which Φ is one-to-one. Find the image under Φ of:
(a) The u- and v-axes
(b) The rectangle R = [−1, 1] × [−1, 1]
(c) The line segment joining (0, 0) and (1, 1)
(d) The triangle with vertices (0, 0), (0, 1), and (1, 1)