The number of oxygen atoms present in chemical formula of fuming sulphuric acid is _______.
The chemical formula for fuming sulfuric acid is $\text{HSO}_3\text{SO}_3$, also known as oleum.
The number of oxygen atoms in the formula is calculated by counting the oxygens in both parts of the formula:
- $\text{HSO}_3$ contributes 3 oxygen atoms. - $\text{SO}_3$ contributes 3 oxygen atoms.
Thus, the total number of oxygen atoms in fuming sulfuric acid is $3 + 3 + 1 = 7$. Therefore, the correct answer is 7.
Let \( S = \left\{ m \in \mathbb{Z} : A^m + A^m = 3I - A^{-6} \right\} \), where
\[ A = \begin{bmatrix} 2 & -1 \\ 1 & 0 \end{bmatrix} \]Then \( n(S) \) is equal to ______.