1. Given two vectors $\boldsymbol{a}, \boldsymbol{b}$ satisfy $|\boldsymbol{a}-2 \boldsymbol{b}|=1,|2 \boldsymbol{a}+3 \boldsymbol{b}|=\frac{1}{3}$, then $(5 \boldsymbol{a}-3 \boldsymbol{b}) \cdot(\boldsymbol{a}-9 \boldsymbol{b})$ is . $\qquad$
1. $\frac{80}{9}$ Detailed explanation: Let $a-2b=m, 2a+3b=n$, then $5a-3b=3m+n, a-9b=3m-n$. Therefore, $(5 \boldsymbol{a}-3 \boldsymbol{b}) \cdot(\boldsymbol{a}-9 \boldsymbol{b})=9|\boldsymbol{m}|^{2}-|\boldsymbol{n}|^{2}=9-\frac{1}{9}=\frac{80}{9}$.