Use the given vectors to find $\mathbf{v} \cdot \mathbf{w}$ and $\mathbf{v} \cdot \mathbf{v}$.
\[
\mathbf{v}=6 \mathbf{i}-3 \mathbf{j}, \mathbf{w}=-2 \mathbf{i}-\mathbf{j}
\]

Step 1 ：Given vectors are \(\mathbf{v}=6 \mathbf{i}-3 \mathbf{j}\), \(\mathbf{w}=-2 \mathbf{i}-\mathbf{j}\)

Step 2 ：The dot product of two vectors can be calculated by multiplying the corresponding components of the vectors and then adding them together. For vectors in 2D, if \(\mathbf{v}=a \mathbf{i}+b \mathbf{j}\) and \(\mathbf{w}=c \mathbf{i}+d \mathbf{j}\), then \(\mathbf{v} \cdot \mathbf{w}=ac+bd\)

Step 3 ：Substitute the given vectors into the formula, we get \(\mathbf{v} \cdot \mathbf{w}=(6*-2)+(-3*-1)\) and \(\mathbf{v} \cdot \mathbf{v}=(6*6)+(-3*-3)\)

Step 4 ：Calculate the above expressions, we get \(\mathbf{v} \cdot \mathbf{w} = -9\) and \(\mathbf{v} \cdot \mathbf{v} = 45\)

Step 5 ：Final Answer: \(\mathbf{v} \cdot \mathbf{w} = \boxed{-9}\) and \(\mathbf{v} \cdot \mathbf{v} = \boxed{45}\)