When a very cold air mass covers half of the united states, a very warm air mass often covers the other half. explain how this happens?

Maritime tropical air masses develop over warm waters present in the tropics and Gulf of Mexico, where heat and moisture are carried to to the overlying air from the water below.

Tropical air masses having northward movement carry warm moist air into the United States, thus increasing the potential for condensation. Generally the southern states experience tropical air masses. But, in winter season, southerly winds ahead of migrating cyclones sometimes transport tropical air mass towards north.

The counterclockwise winds related to northern hemisphere mid latitude cyclones play an important role in the movement air masses, carrying warm moist air towards north ahead of a low while dragging colder and drier air towards south.