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how to tell if you have a yeast infection - Professionaloutdoormedia

📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 Scaling by 2 multiplies the entire transformation matrix by 2:

📌 \mathbf{M} = 2 egin{pmatrix} 0 & -1 \ 1 & 0 \end{pmatrix} = egin{pmatrix} 0 & -2 \ 2 & 0 \end{pmatrix}

📌 Thus, the required matrix is \(oxed{egin{pmatrix} 0 & -2 \ 2 & 0 \end{pmatrix}}\).

📌 A civil engineer analyzing directional stability in solar panel arrays needs to find a vector \(\mathbf{v}\) such that \(\mathbf{v} imes egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} = egin{pmatrix} 0 \ 0 \ 5 \end{pmatrix}\), where the cross product is defined in 3D. Find a suitable \(\mathbf{v}\).

📌 Let \(\mathbf{v} = egin{pmatrix} x \ y \ z \end{pmatrix}\), \(\mathbf{a} = egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}\), and \(\mathbf{v} imes \mathbf{a} = egin{pmatrix} 0 \ 0 \ 5 \end{pmatrix}\).

📌 \mathbf{v} imes \mathbf{a} = egin{vmatrix}

📌 \end{vmatrix} = \mathbf{i}(y \cdot 3 - z \cdot 2) - \mathbf{j}(x \cdot 3 - z \cdot 1) + \mathbf{k}(x \cdot 2 - y \cdot 1)

📌 = egin{pmatrix} 3y - 2z \ - (3x - z) \ 2x - y \end{pmatrix} = egin{pmatrix} 3y - 2z \ -3x + z \ 2x - y \end{pmatrix}

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