Can delinquent be used to describe something like a school assignment?
You still have some delinquent assignments.
Or does the word only apply to monetary matters?
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The word delinquent does not only apply to monetary matters.
While the noun delinquent refers to a young offender, the adjective is more forgiving. In AmE, bills in arrears are most commonly marked 'delinquent' by credit agencies.
If you are writing for an AmE audience, I think it is quite appropriate to label one's missing homework as delinquent; in fact, doing so would give the statement an air of gravity and connote a failure in responsibility to a far greater extent than missing, late, or in arrears. Having said that, it is traditionally more common to refer to them as overdue. Your choice depends on what you wish to connote in delivering your information.
The OED stipulates that the adjective, in North America, means in arrears, from the L. verb delinquere, from de- 'away' + linquere 'to leave'.
delinquent adjective 1. failing in or neglectful of a duty or obligation; guilty of a misdeed or offense. 2. (of an account, tax, debt, etc.) past due; overdue.
also 1. (Law) guilty of an offence or misdeed, esp one of a minor nature 2. (Law) failing in or neglectful of duty or obligation
also The failure to accomplish what is required by law or duty, such as the failure to make a required payment or to perform a certain action.
"Delinquent" generally applies to people rather than things. So, one can certainly be delinquent in submitting one's school assignments. Even applying it to a bill would be suspect, though an account might be delinquent in so far as "account" can refer to the person or group holding it. The account itself might be "in arrears" (formally). In any case, the assignments should just be "overdue" or just "late."