A region R in the xy-plane is given. Find equations for a transformation T that maps a rectangular region S in the uv-plane onto R, where the sides of S are parallel to the u- and v- axes. (Let u play the role of r and v the role of θ. Enter your answers as a comma-separated list of equations.) R lies between the circles x^2 + y^2 = 1 and x^2 + y^2 = 3 in the first quadrant

Fill in the blank 1. a rhombus is a rectangle a) always b) sometimes c) never 2. a square is a quadrilateral a) always b) sometimes c) never 3. a trapezoid is a kite a) always b) sometimes c) never 4. a quadrilateral is a kite a) always b) sometimes c) never 5. a square is a rhombus a) always b) sometimes c) never 6. a parallelogram is a rectangle a) always b) sometimes c) never