// Numbas version: finer_feedback_settings
{"name": "Adaptive marking: rotation matrix", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"rad_rotation": {"name": "rad_rotation", "description": "<p>Angle of rotation in radians</p>", "templateType": "anything", "group": "Rotation matrix", "definition": "radians(rotation)"}, "det_m": {"name": "det_m", "description": "", "templateType": "anything", "group": "Rotation matrix", "definition": "det(mat)"}, "mat": {"name": "mat", "description": "<p>Rotation matrix for the given rotation</p>", "templateType": "anything", "group": "Rotation matrix", "definition": "matrix([\n  [cos(rad_rotation),-sin(rad_rotation)],\n  [sin(rad_rotation),cos(rad_rotation)]\n])"}, "rotation": {"name": "rotation", "description": "<p>Angle of rotation in degrees</p>", "templateType": "anything", "group": "Rotation matrix", "definition": "random(10..90)"}}, "variable_groups": [{"name": "Rotation matrix", "variables": ["rotation", "rad_rotation", "mat", "det_m"]}], "parts": [{"gaps": [{"correctAnswerFractions": false, "numRows": "2", "scripts": {}, "marks": "4", "precisionType": "dp", "precisionPartialCredit": 0, "variableReplacements": [], "showCorrectAnswer": true, "markPerCell": true, "allowResize": false, "type": "matrix", "strictPrecision": false, "allowFractions": false, "correctAnswer": "mat", "precision": "2", "numColumns": "2", "tolerance": 0, "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacementStrategy": "originalfirst"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "variableReplacements": [], "type": "gapfill", "prompt": "<p>Write a matrix $\\mathrm{M}$ corresponding to a rotation of $\\var{rotation}^{\\circ}$ anti-clockwise about the origin.</p>\n<p>Round numbers to 2 decimal places.</p>\n<p>$\\mathrm{M} = $&nbsp;[[0]]</p>", "variableReplacementStrategy": "originalfirst"}, {"gaps": [{"maxValue": "det(mat)", "correctAnswerFraction": false, "precision": "2", "showPrecisionHint": false, "marks": 1, "precisionType": "dp", "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacements": [{"part": "p0g0", "variable": "mat"}], "strictPrecision": false, "type": "numberentry", "scripts": {}, "allowFractions": false, "minValue": "det(mat)", "precisionPartialCredit": 0, "variableReplacementStrategy": "originalfirst"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "variableReplacements": [], "type": "gapfill", "prompt": "<p>$\\operatorname{det}\\mathrm{M} = $&nbsp;[[0]] (Round your answer to 2 decimal places)</p>", "variableReplacementStrategy": "originalfirst"}, {"gaps": [{"correctAnswerFractions": false, "numRows": "2", "scripts": {}, "marks": 1, "precisionType": "dp", "precisionPartialCredit": 0, "variableReplacements": [{"part": "p0g0", "variable": "mat"}, {"part": "p1g0", "variable": "det_m"}], "showCorrectAnswer": true, "markPerCell": false, "allowResize": false, "type": "matrix", "strictPrecision": false, "allowFractions": false, "correctAnswer": "matrix([[mat[1][1],-mat[0][1]],[-mat[1][0],mat[0][0]]])/det_m", "precision": "2", "numColumns": "2", "tolerance": 0, "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacementStrategy": "originalfirst"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "variableReplacements": [], "type": "gapfill", "prompt": "<p>$\\mathrm{M}^{-1} = $&nbsp;[[0]]</p>\n<p></p>", "variableReplacementStrategy": "originalfirst"}], "functions": {}, "showQuestionGroupNames": false, "tags": [], "ungrouped_variables": [], "name": "Adaptive marking: rotation matrix", "preamble": {"js": "", "css": ""}, "metadata": {"description": "<p data-bind=\"html: 'hi'\">Ask the student to find a&nbsp;matrix corresponding to a given rotation about the origin.</p>\n<p data-bind=\"html: 'hi'\">Then ask them to find the determinant. Their answer is marked against the matrix they gave, not just the correct one.</p>\n<p data-bind=\"html: 'hi'\">Finally, ask them to find the inverse of their matrix. Marking is&nbsp;against the matrix and determinant they gave.</p>", "notes": "", "licence": "Creative Commons Attribution 4.0 International"}, "question_groups": [{"pickQuestions": 0, "pickingStrategy": "all-ordered", "questions": [], "name": ""}], "type": "question", "statement": "", "variablesTest": {"maxRuns": 100, "condition": ""}, "advice": "", "rulesets": {}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}