What happens to the equation 𝑥2+𝑦2=𝑟2 in a rotated 𝑥′𝑦′−system?Group of answer choicesIn a rotated 𝑥′𝑦′-system, 𝑥′ replaces 𝑥 and 𝑦′ replaces 𝑦.In a rotated 𝑥′𝑦′-system, 1 replaces 𝑥 and 1 replaces 𝑦.In a rotated 𝑥′𝑦′-system, 1 replaces and 𝑦′ replaces 𝑦.In a rotated 𝑥′𝑦′-system, 𝑥′ replaces 𝑥 and 1 replaces 𝑦.

Although the algebra of rotations can get ugly, the main idea is that rotation through an appropriate angle will transform a general second-degree equation into an equation in 𝑥′ and 𝑦′ without an 𝑥′𝑦′−term.Group of answer choicesTrueFalse

Which of the following is true for matrices?Question 1Select one: (𝐴𝑇) = 𝐴 (𝐴𝐵)-1 = 𝐵-1𝐴-1 𝐴*𝐼 = 𝐴𝐴𝐵=𝐵𝐴

If lim𝑥→2𝑓(𝑥)=3𝑥 and lim𝑥→2𝑔(𝑥)=4𝑥2−5, what is lim𝑥→2𝑔(𝑓(𝑥))?

Given that𝑓(𝑥)=2𝑥−3 and 𝑔(𝑥)=1−𝑥4solve (𝑓∘𝑔−1)(𝑥)=(𝑓∘𝑔)(𝑥).

Which of the following transformations produces an image that has the same orientation (faces the same way) as the pre-image?Group of answer choicesRotation and TranslationScratchRotation and ReflectionScratchReflection onlyScratchTranslation onlyScratch