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Home » 10 Shocking Truths About Pearl Jam Members You’ve Never Heard Before! - Crankk.io

10 Shocking Truths About Pearl Jam Members You’ve Never Heard Before! - Crankk.io

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 R = egin{pmatrix} 0 & -1 \ 1 & 0 \end{pmatrix}

📌 A vector \(\mathbf{v} = egin{pmatrix} x \ y \end{pmatrix}\) is invariant under \(R\) if:

📌 R\mathbf{v} = egin{pmatrix} 0 & -1 \ 1 & 0 \end{pmatrix} egin{pmatrix} x \ y \end{pmatrix} = egin{pmatrix} -y \ x \end{pmatrix} = egin{pmatrix} x \ y \end{pmatrix}

📌 -y = x \quad ext{and} \quad x = y

📌 From \( -y = x \) and \( x = y \), substituting: \( -x = x \Rightarrow x = 0 \), then \( y = 0 \). Only solution is \(\mathbf{v} = egin{pmatrix} 0 \ 0 \end{pmatrix}\), but \( \|\mathbf{v}\|^2 = 0

📌 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.

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\(r = 5\) cm (radius),
\(l = 13\) cm (slant height),
\(\pi \approx 3.14\)
Calculate each part:
\pi r^2 = 3.14 \times 5^2 = 3.14 \times 25 = 78.5 \text{ cm}^2
\pi r l = 3.14 \times 5 \times 13 = 3.14 \times 65 = 204.1 \text{ cm}^...
Add them together:
A = 78.5 + 204.1 = 282.6 \text{ cm}^2
Thus, the total surface area of the cone is:
\boxed{282.6 \text{ cm}^2}

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