Tina is studying at . . . . . . . . university in . . . . . . . . U.S.A.

The first blank will be filled with the indefinite article 'a'. Though the word following the blank starts with the vowel 'u' but as the word 'university' starts with a consonant sound, 'a' shall be used in the first blank.
And whenever 'U.S.A.' is mentioned, the definite article 'the' comes before it.