If rent pay day is the first of the month, and the landlord gave notice (which needed to be written) on June 2, then you do not have to leave until the last day in July. It is 30 days from the next rent due day, and the next one is July 1. This is per the Arizona Residential Landlord-Tenant Act, which the landlady must abide by whether she likes it or not. There are also procedures for protecting your security deposit in the Az L-T Act.
If, however, the second depo is taken by the same party, and the questions really are repetitive, the objection is asked and answered. Do not go in without a lawyer. Many cases are lost because of words spoken in depos.