Name the basic gate that is equivalent to two NOR gates connected in series.

OR gate. A NOR gate with a repeated (single) input acts as a NOT gate: $NOR(X,X) = (X+X)'=X'$. So the first NOR gate gives $N_1=(A+B)'$, and the second NOR gate, with both its inputs tied to $N_1$, gives $N_1' = ((A+B)')' = A+B$. Hence two NOR gates in series (the second used as an inverter) are equivalent to a single OR gate.