1.5. consider a 2d rectangular test area r with vertices (1; 1), (3; 1), (1; 4), and (3; 4). the velocity field is f(x; y) = [y x]t . 1. sketch the vector field in the first quadrant in and surrounding r. 2. compute the net outward flux through the boundary of ¶r: r ¶r f nds.

Let v1, v2, w be three linearly independent vectors in r 3 . that is, they do not all lie on the same plane. for each of the following (infinite) set of vectors, carefully sketch it in r 3 , and determine whether or not it is a vector space (i.e., a subspace of r 3 ). explain your reasoning

The electric potential v is constant everywhere within a certain region of space. which statement below is true? the choices are: the electric field is also constant (but not zero) within the region. a charged particle placed within the region will experience an electric force. the electric field is zero everywhere within the region. the electric field varies from place to place within the region.

Acoil suspended freely, points in some direction when no current is passed through it . can you tell what will happen when a current is passed though it?