If the president needed to settle a diplomatic situation with great britain, which cabinet position would most likely be sent carry out the mission

In such a diplomatic situation, the Secretary of State would be sent. Handling international relations is the primary job of the U.S. Secretary of State.

the tariff was created to protect industry in the northern part of the united states. industries in the north were being driven out of business by imported goods that were priced at a low rate. the goal was to protect these industries   by taxing the goods.

to protest slavery i would think it would be a