Match the vector fields F with the plots labeled I-IV. Give reasons for each of your choices. F(x, y) = (y, x) F(x, y) = (1, sin y) F(x, y) = (x - 2, x + 1) F(x, y) = (y, 1/x) For each of the...

Match the vector fields F with the plots labeled I-IV. Give reasons for each of your choices. F(x, y) = (y, x) F(x, y) = (1, sin y) F(x, y) = (x - 2, x + 1) F(x, y) = (y, 1/x) For each of the following vector fields F, compute the function rot(F). Then give a one sentence description of what the vector field would look like if you plotted it. F(x, y) = (x, y) F(x, y) = y i = x j F(x, y) = (y, -x) F(x, y) = (1 + xy)i + x^2 sin y j F(x, y) = (x, xy)