Suppose we changed the units of the tuition variable, so that the new tuition variable is now simply measured in dollars rather than in thousands of dollars. What would happen to the correlation between tuition (in dollars) and number of applicants?

The correlation would stay the same, because chainging the measure from thousands of dollars to simply dollars only modifies the nominal values of tuition.

For example, instead of having tuition cost 300 thousand dollars, now it costs 300,000 dollars. The real value, that is to say, the real cost, is the same, and the correlation between applicants and the cost of tuition depends on the real value, not on the nominal value.