{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"f001020e-9b7b-56f7-8157-dcd5f386ce8d","task_key":"precalculus--test--f001020e-9b7b-56f7-8157-dcd5f386ce8d","task_revision_id":"1","upstream_id":"","short_description":"Let $\\mathbf{D}$ be a matrix representing a dilation with scale factor $k > 0,$…","config":"precalculus","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"Let $\\\\mathbf{D}$ be a matrix representing a dilation with scale factor $k > 0,$ and let $\\\\mathbf{R}$ be a matrix representing a rotation about the origin by an angle of $\\\\theta$ counter-clockwise.  If\\n\\\\[\\\\mathbf{D} \\\\mathbf{R} = \\\\begin{pmatrix} -7 & 1 \\\\\\\\ -1 & -7 \\\\end{pmatrix},\\\\]then find $k.$\",\"type\":\"Precalculus\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}