If a person is an exempt employee(salaried) in RI, Is the employer required by law to pay that entire weekly salary if less than 40 hours are worked?

In most cases, yes. However, there are exceptions.

An exempt employee can legally have their wages docked in the following situations:

1.) It is either the first or last week of employment and the employee does not work the entire week
2.) The employee is on FMLA
3.) The employer provides a reasonable number of paid sick days; the employee either has used all the days available to him or is not yet eligible for them, and calls in sick
4.) The employee takes a day off for personal reasons (regardless of whether vacation or personal time is provided/available or not)
5.) The employee has been suspended for a major safety violation
6.) The employee has been suspended for violation of a written company policy which applies to all employees and which relates to workplace conduct (sexual harassment, violence in the workplace, drugs/alcohol on the work premises, etc.)