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Home » Shaded area is \( 144 - 36\pi \) cm². - Decision Point

Shaded area is \( 144 - 36\pi \) cm². - Decision Point

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Thus, no non-zero integer vector satisfies both invariance and norm condition.

📌 But wait â reconsider: âinvariant under \(90^\circ\) rotationâ means \( R\mathbf{v} = \mathbf{v} \), which we solved gives \( x = -y \) and \( x = y \Rightarrow x = 0, y = 0 \). So only trivial fixed vector.

📌 Alternatively, if the problem meant vectors that are *cyclically ordered* under symmetry, but the wording specifies âinvariant under a \(90^\circ\) rotationâ, so must satisfy \( R\mathbf{v} = \mathbf{v} \).

📌 Thus, only solution is \(\mathbf{v} = (0,0)\), which does not satisfy \(\|\mathbf{v}\|^2 = 10\).

📌 Hence, the

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