Final answer:
The sentence "the oldest military academy in the United States and one of the most prestigious" is a phrase, as it lacks a subject and a verb, which are necessary components of a clause.
Step-by-step explanation:
The sentence in question, "the oldest military academy in the United States and one of the most prestigious," is not a full sentence, but rather a phrase. This is because it lacks a subject performing an action (verb). Phrases are part of sentences that can function as a unit but do not have both a subject and a verb that form a complete thought. A clause, in contrast, contains both a subject and a verb.
In this context, the phrase is providing descriptive information that could be used in a larger sentence, such as in "It is the oldest military academy in the United States and one of the most prestigious." Here, "It is" would be the clause, and the phrase in question functions as the predicate that describes the subject 'It'.