Final answer:
To eliminate the xy-term in the equation x*y = 8 using a rotation of axes, we can rotate the coordinate system by an angle θ such that the new axes align with the x and y axes of the original system.
Step-by-step explanation:
To eliminate the xy-term in the equation x*y = 8 using a rotation of axes, we can rotate the coordinate system by an angle θ such that the new axes align with the x and y axes of the original system. Let's assume the new axes are represented by x' and y'.
Since we want to eliminate the xy-term, we need to choose an angle θ such that the equation remains the same when expressed in terms of x' and y'. In this case, we can choose θ such that the equation becomes x'y' = 8.
By applying the appropriate rotation matrix to the original equation, we can find the new equation x'y' = 8. This transformation allows us to eliminate the xy-term.