Where in the US are these vowels mispronounced? "got" -> "gat"

/a/ ⟹ /æ/ is part of the ongoing sound change now occurring in northern urban speech groups in American English called the Northern Cities Vowel Shift.

This is a big change in English vowels, as complex and thorough as the Great Vowel Shift that moved all the long vowels in English but left the short ones in the same place, thus producing Early Modern English from Middle English.

Diagrams and examples of both of these shifts are available here.

The Northern Cities Shift been a focus of study by sociolinguists for several decades. It also includes a number of other pronunciation variants that you may be familiar with, as shown on the charts.