The solutions that will form a precipitate when mixed with aqueous sodium carbonate are:
\[
\boxed{\text{Copper(II) nitrate, } \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq})}
\]
\[
\boxed{\text{Silver nitrate, } \mathrm{AgNO}_{3}(\mathrm{aq})}
\]