Has, Have---need help

-The tomatoes have grown quickly this year.

-The lettuce has grown quickly too.

Why do one use HAVE and the other one use HAS

-The new supermarket has everything.
-Mr. and Mrs Smith and their son have gone to Sweden for the week.

i don't know when to use have or has.
can somebody help me out.

Thank you

Hi Melaine!
Although i am learning english as a second language, i will try to explain your problem.
Well your problem is related to "Subject-verb agreement". In every sentence subject and verb should agree with each other. Remember that Have is a plural auxiliary verb and Has is singular. So whenever there is a plural subject you have to use "have" and for singluar subject "has" should be used.
"The tomatoes have grown quickly this year"
Here subject is tomatoes which is definitely plural therefore we use auxiliary verb"have".

The lettuce has grown quickly too.

Lettuce is singular and it requires a singular auxiliary verb"has".

The new supermarket has everything.

Subject"the new supermarket" is singular.

Mr and Mrs Smith and their son have gone to Sweden for the week.
Here subject is "Mr and Mrs Smith and their son" which is a plural subject so we have to use a plural auxiliary verb

have.
Also remember that
Ist person singular ----- I have
2nd person singular----- You have
3rd person Singurlar---- he ,she,it or any person has

1st person plural ----- we have
2nd person plural ----- you have
3rd person plural ----- they have

This is a big help. Thank you so much Atesttaker and everyone else who had helped me.