Sketch a plot of the vector field
F = - x / (1 + x2 + y2)3/2 i - y / (1 + x2 + y2)3/2 j
for (x, y) in the rectangle -1 s x s 1, -1 s y s 1. From the plot, use the marginal box that describes the interpretation of div and curl to determine whether div is positive, negative, or zero at the origin, and whether a paddle wheel placed at the origin would rotate clockwise, counterclockwise, or not at all. (For the curl, think of F as being a vector field in 3-space with z-component equal to 0.)