Is copper (2) nitrate and ammonium hydroxide a physical change?

No. It is a chemical change (chemical reaction) in which the products are different from the reactants. The balanced chemical equation is Cu(NO3)2+2NH4OH-->Cu(OH)2+2NH4NO3, which means one mole of copper(II) nitrate plus two moles of ammonium hydroxide produce one mole of copper(II) hydroxide plus two moles of ammonium nitrate.