Step 1 :The submarine is initially at an elevation of \(-355 \frac{2}{7}\) feet. It then dives downward an additional \(-92 \frac{4}{7}\) feet.
Step 2 :To find the new elevation, we need to add these two values. Since both values are negative (representing depths below sea level), the result will be a larger negative number.
Step 3 :\(-355 \frac{2}{7} + -92 \frac{4}{7} = -447 \frac{6}{7}\)
Step 4 :Final Answer: The new elevation of the submarine is \(\boxed{-447 \frac{6}{7}}\) feet.