Hover Tank: Some lighter tanks are, indeed, vector-control vehicles which can hover (and fly briefly to hop over obstacles, although using this as an extended flight capability is discouraged, due to the high probability of a fatal encounter with a real aircraft).  Their strengths are in speed and maneuver (and, of course, the side-to-side strafe), but they’re relatively fragile and have to stick to relatively light weapons lest they burn lots of fuel counteracting weapon recoil, etc., so their main usage is in the scouting/harassment/fast-attack role.  Main battle tanks are still the traditional heavy, tracked vehicle.

While the trope disclaims these as being members, they were preceded by military hovercraft in a more restricted version of the same role.