Given the following scalar potentials (V), calculate the solution for the gradient of V (∇V), and plot the vector arrow representation of this vector field over the given limits. a. V = 15+ r cosΦ, for 0 <= r <= 10, and 0 <= Φ 2π. b. V = 100+ xy, for -- 10 <= x <=10

If you were designing a bumper for a car, would you prefer it to exhibit elastic or plastic deformation? why? consider the functions of a bumper in both a minor "fender-bender" and a major collision.

Which of the following is an easy way to remember the modified “x” tire rotation? a. nondrive wheels straight, cross the drive wheels b. drive wheels straight, cross the nondrive wheels c. drive wheels crossed, nondrive wheels straight d. drive wheels crossed, nondrive wheels crossed

Slip occurs via two partial dislocations because of (a) the shorter path of the partial dislocation lines; (b) the lower energy state through partial dislocations; (c) the charge balance.