Which of the following is correct according to the rule of collective nouns:
- A fleet of cars are parked.
- A fleet of car are parked.
- A fleet of car is parked.
A fleet of cars is parked.
Why? It might help to consider the sentence without the prepositional phrase:
A fleet ... is parked.
While a fleet of cars is many cars, our sentence is describing only one "fleet". Consider also:
The team is at the stadium
A team is made up of many people, but the team itself is one item. We can add a prepositional phrase:
The team of football players is at the stadium
And see that we still use "is" instead of "are".
UPDATE: As pointed out in the comments, this answer is primarily for American English. British English allows either, but to an American (like me) the example sentence of "my family are" sounds quite strange.
cars is a counting noun, hence 'cars'. However, like Noah said, what you are really talking about is the 'fleet', so 'A fleet of cars is parked' is correct.
However, in spoken English, where the rules are fast and loose, you might often hear this said as: "A fleet of cars are parked" because of the similar sentence: "The cars are parked", which wouldn't sound wrong.