what is the velocity of a 1,000 kg cannon that shoots 10 kg bullets at a speed of 380 m/s?

well, lets assume it is standing still and then shoots one round.

The total momentum remains zero so
0 = 1000 v + 10 * 380
v = -3800/1000
v = - 3.8 m/s

The negative sign means the cannon moves backwards if the bullet moves forwards (what else is new?)