$7.$ Two cars collide at an intersection. Car A $(1200$ kg$)$ is traveling east at $25$ m$/$s$,$ and car B $(1500$ kg$)$ is traveling north at $15$ m$/$s$.$ After the collision, the cars stick together.

$$ a$.$ Calculate the velocity $($magnitude and direction$)$ of the cars immediately after the collision.

$$ b$.$ Determine the loss of kinetic energy during the collision.