From 004781bdedf3d14032c65ea91197b64aad12ecae Mon Sep 17 00:00:00 2001 From: Wang Weiye Date: Tue, 18 Oct 2022 17:50:12 +0800 Subject: [PATCH] 20221018 afternoon --- 工具/关键字筛选题号.ipynb | 12 +++++------ 工具/寻找阶段末尾空闲题号.ipynb | 8 ++++---- 工具/已用题号剔除.ipynb | 14 ++++++------- 工具/文本文件/题号筛选.txt | 6 +++--- 工具/添加关联题目.ipynb | 4 ++-- 工具/讲义生成.ipynb | 10 +++++----- 工具/题号选题pdf生成.ipynb | 16 +++++++-------- 题库0.3/Problems.json | 35 ++++++++++++++++++++++++++++++--- 8 files changed, 67 insertions(+), 38 deletions(-) diff --git a/工具/关键字筛选题号.ipynb b/工具/关键字筛选题号.ipynb index 4b8a13ac..06a6c669 100644 --- a/工具/关键字筛选题号.ipynb +++ b/工具/关键字筛选题号.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 17, + "execution_count": 3, "metadata": {}, "outputs": [ { @@ -11,7 +11,7 @@ "0" ] }, - "execution_count": 17, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" } @@ -21,7 +21,7 @@ "\n", "\"\"\"---设置关键字, 同一field下不同选项为or关系, 同一字典中不同字段间为and关系, 不同字典间为or关系, _not表示列表中的关键字都不含, 同一字典中的数字用来供应同一字段不同的条件之间的and---\"\"\"\n", "keywords_dict_table = [\n", - " {\"tags\":[\"五\"]}\n", + " {\"tags\":[\"六\"],\"content\":[\"所成的角\",\"perp\",\"垂直\",\"平行\",\"parallel\"]}\n", "]\n", "\"\"\"---关键字设置完毕---\"\"\"\n", "# 示例： keywords_dict_table = [\n", @@ -85,7 +85,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -99,12 +99,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.7" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" } } }, diff --git a/工具/寻找阶段末尾空闲题号.ipynb b/工具/寻找阶段末尾空闲题号.ipynb index f4b89672..094796ad 100644 --- a/工具/寻找阶段末尾空闲题号.ipynb +++ b/工具/寻找阶段末尾空闲题号.ipynb @@ -11,7 +11,7 @@ "text": [ "首个空闲id: 11988 , 直至 020000\n", "首个空闲id: 20227 , 直至 030000\n", - "首个空闲id: 30154 , 直至 999999\n" + "首个空闲id: 30169 , 直至 999999\n" ] } ], @@ -45,7 +45,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -59,12 +59,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.7" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" } } }, diff --git a/工具/已用题号剔除.ipynb b/工具/已用题号剔除.ipynb index becc5673..fecfa53f 100644 --- a/工具/已用题号剔除.ipynb +++ b/工具/已用题号剔除.ipynb @@ -2,15 +2,15 @@ "cells": [ { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "首行题目数量: 1236\n", - "剩余题目数量: 1092\n" + "首行题目数量: 393\n", + "剩余题目数量: 337\n" ] } ], @@ -22,7 +22,7 @@ "\"\"\"---设置题号列表文件结束---\"\"\"\n", "\n", "\"\"\"---设置要排除的题号所在的绝对路径---\"\"\"\n", - "mainpath = r\"C:/Users/Weiye/Documents/wwy sync/23届/\"\n", + "mainpath = r\"C:/Users/wang Weiye/Documents/wwy sync/23届/\"\n", "\n", "used_path_list = [\n", "mainpath + \"第一轮复习讲义/\",\n", @@ -84,7 +84,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -98,12 +98,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.7" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" } } }, diff --git a/工具/文本文件/题号筛选.txt b/工具/文本文件/题号筛选.txt index f2230473..cf58c046 100644 --- a/工具/文本文件/题号筛选.txt +++ b/工具/文本文件/题号筛选.txt @@ -1,7 +1,7 @@ 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未使用题号: -000138,000143,000144,000145,000146,000147,000148,000149,000151,000152,000154,000155,000156,000157,000158,000160,000161,000162,000164,000167,000171,000172,000173,000366,000382,000390,000396,000401,000405,000422,000427,000438,000447,000460,000469,000490,000502,000509,000529,000535,000554,000566,000571,000598,000609,000618,000628,000649,000653,000662,000677,000687,000699,000701,000718,000732,000763,000777,000785,000817,000819,000831,000838,000847,000855,000872,000881,000900,000919,000930,000933,000936,000947,000953,000955,000973,001849,001851,001854,001855,001859,001861,001862,001865,001866,001867,001868,001872,001873,001874,001875,001876,001878,001879,001880,001881,001883,001884,001885,001887,001890,001891,001893,001897,001899,001900,001901,001903,001904,001908,001909,001915,001917,001994,001995,001996,001997,001998,002002,002003,002005,002006,002009,002011,002014,002015,002019,002021,002022,002023,002024,002028,002029,002030,002031,002033,002034,002035,002036,002037,002039,002040,002041,002042,002043,002044,002045,002046,002047,002048,002049,002050,002051,002052,002053,002054,002055,002056,002058,002059,002060,002061,002062,002063,002064,002065,002066,002067,002068,002069,002070,002071,002072,002073,002074,002075,002076,002077,002078,002079,002080,002081,002082,002083,002084,002087,002089,002090,002091,002092,002093,002094,003326,003329,003333,003334,003335,003336,003338,003339,003340,003342,003344,003348,003349,003350,003351,003352,003353,003354,003357,003358,003359,003360,003503,003504,003506,003507,003509,003511,003512,003513,003515,003516,003518,003525,003526,003527,003529,003530,003531,003532,003533,003536,003537,003539,003540,003541,003543,003545,003546,003547,003548,003549,003552,003553,003589,003592,003612,003632,003633,003656,003677,003702,003722,003723,003725,003762,003771,003784,003794,003808,003820,003821,003836,003841,003847,003853,003864,003866,003871,003872,003878,003880,003888,003901,003908,003915,003922,003926,003940,003946,003949,003955,003961,003967,004069,004072,004081,004090,004101,004113,004126,004132,004145,004160,004162,004176,004185,004194,004199,004206,004208,004219,004222,004233,004253,004258,004279,004301,004302,004307,004315,004319,004325,004337,004471,004477,004481,004485,004489,004490,004498,004503,004512,004518,004543,004556,004621,004634,004641,004688,004692,004703,004706,004725,004733,004745,004754,006992,006993,006994,006995,006996,006997,006998,006999,007000,007001,007002,007003,007004,007005,007006,007007,007008,007009,007010,007011,007012,007013,007014,007015,007016,007017,007018,007019,007020,007021,007022,007023,007024,007025,007026,007027,007028,007029,007030,007031,007032,007033,007034,007035,007036,007037,007038,007039,007040,007041,007042,007043,007044,007045,007046,007047,007048,007049,007050,007051,007052,007053,007054,007055,007056,007057,007058,007059,007060,007061,007062,007063,007064,007065,007066,007067,007068,007069,007070,007071,007072,007073,007074,007075,007076,007077,007078,007079,007080,007081,007082,007083,007084,007085,007086,007087,007088,007089,007090,007091,007092,007093,007094,007095,007096,007097,007098,007099,007100,007101,007102,007103,007104,007105,007106,007107,007108,007109,007110,007111,007112,007113,007114,007115,007116,007117,007118,007119,007120,007121,007122,007123,007124,007125,007126,007127,007128,007129,007130,007131,007132,007133,007134,007135,007136,007137,007138,007139,007140,007141,007142,007143,007144,007145,007146,007147,007148,007149,007150,007151,007152,007153,007154,007155,007156,007157,007158,007159,007160,007161,007162,007163,007164,007165,007166,007167,007168,007169,007170,007171,007172,007173,007174,007175,007176,007177,007178,007179,007180,007181,007182,007183,007184,007185,007186,007187,007188,007189,007190,007191,007192,007193,007194,007195,007196,007197,007198,007199,007200,007201,007202,007203,007204,007205,007206,007207,007208,007209,007210,007211,007212,007213,007214,007215,007216,007217,007218,007219,007220,007221,007222,007223,007224,007225,007226,007227,007228,007229,007230,007231,007232,007233,007234,007235,007236,007237,007238,007239,007240,007241,007242,007243,007244,007245,007246,007247,007248,007249,007250,007251,007252,007253,007254,007255,007256,007257,007258,007259,007260,007261,007262,007263,007264,007265,007266,007267,007268,007269,007270,007271,007272,007273,007274,007275,007276,007277,007278,007279,007280,007281,007282,007283,007284,007285,007286,007287,007288,007289,007290,007291,007292,007293,007294,007295,007296,007297,007298,007299,007300,007301,007302,007303,007304,007305,007306,007307,007308,007309,007310,007311,007312,007315,007316,007317,007318,007319,007320,007321,007322,007323,007324,007325,007326,007327,007328,007329,007330,007331,007332,007333,007334,007335,007336,007337,007338,007339,007340,007341,007342,007343,007344,007345,007346,007347,007348,007349,007350,007351,007352,008544,008545,008546,008547,008548,008549,008550,008551,008552,008553,008554,008555,008556,008557,008558,008559,0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已使用题号: -000139,000140,000141,000142,000150,000153,000159,000163,000165,000166,000168,000169,000170,000174,000328,000339,000348,000354,000387,000414,000477,000481,000515,000557,000637,000760,000788,000792,000858,000871,000883,000892,000894,000902,001846,001847,001848,001850,001852,001853,001856,001857,001858,001860,001863,001864,001869,001870,001871,001877,001882,001886,001888,001889,001892,001894,001895,001896,001898,001902,001905,001906,001907,001910,001911,001912,001913,001914,001916,001992,001993,001999,002000,002001,002004,002007,002008,002010,002012,002013,002016,002017,002018,002020,002025,002026,002027,002032,002038,002057,002085,002086,002088,003327,003328,003330,003331,003332,003337,003341,003343,003345,003346,003347,003355,003356,003361,003501,003502,003505,003508,003510,003514,003517,003519,003520,003521,003522,003523,003524,003528,003534,003535,003538,003542,003544,003550,003551,003621,003703,003758,003798,004116,004167,007313,007314,009032,030106,030107,030108,030109,030110,030152,030153 \ No newline at end of file +000188,000189,000207,000212,000300,000331,000364,000749,001597,001611,001620,001628,001636,001641,001645,001649,001659,001670,001695,001712,003454,003466,003875,003982,004539,004696,009137,009144,009158,009181,009183,009186,009202,009210,009686,009690,009694,009696,009716,009868,010435,010454,010510,010531,030111,030112,030143,030144,030145,030147,030148,030149,030150,030151,030161,030164 \ No newline at end of file diff --git a/工具/添加关联题目.ipynb b/工具/添加关联题目.ipynb index 1f98b5f3..e44b98f5 100644 --- a/工具/添加关联题目.ipynb +++ b/工具/添加关联题目.ipynb @@ -9,8 +9,8 @@ "import os,re,json,time\n", "\n", "\"\"\"---设置原题目id与新题目id---\"\"\"\n", - "old_id = \"9191\"\n", - "new_id = \"30159\"\n", + "old_id = \"167\"\n", + "new_id = \"30169\"\n", "\"\"\"---设置完毕---\"\"\"\n", "\n", "old_id = old_id.zfill(6)\n", diff --git a/工具/讲义生成.ipynb b/工具/讲义生成.ipynb index 3a031540..ad191652 100644 --- a/工具/讲义生成.ipynb +++ b/工具/讲义生成.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": {}, "outputs": [ { @@ -13,9 +13,9 @@ "题块 1 处理完毕.\n", "正在处理题块 2 .\n", "题块 2 处理完毕.\n", - "开始编译教师版本pdf文件: 临时文件/24_体积及表面积的计算_教师_20221017.tex\n", + "开始编译教师版本pdf文件: 临时文件/24_体积及表面积的计算_教师_20221018.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/24_体积及表面积的计算_学生_20221017.tex\n", + "开始编译学生版本pdf文件: 临时文件/24_体积及表面积的计算_学生_20221018.tex\n", "0\n" ] } @@ -55,8 +55,8 @@ "\n", "\"\"\"---设置题号数据---\"\"\"\n", "problems = [\n", - "\"10500,3475,9207,9211,9731,9400,9399,4994,9868,10524,9210,9720,202,10517,4196\",\n", - "\"10498,4084,215,411,11332,212,10499,10519,10522,9209,10515,201,10521\"\n", + "\"10500,3475,30160,30161,30162,30163,30164,4994,9868,10524,9210,9720,202,30165,4196\",\n", + "\"10498,4084,215,411,11332,212,10499,30166,30167,30168,10515,201,10521\"\n", "]\n", "\"\"\"---设置题号数据结束---\"\"\"\n", "\n", diff --git a/工具/题号选题pdf生成.ipynb b/工具/题号选题pdf生成.ipynb index 049a0130..66904e34 100644 --- a/工具/题号选题pdf生成.ipynb +++ b/工具/题号选题pdf生成.ipynb @@ -2,16 +2,16 @@ "cells": [ { "cell_type": "code", - "execution_count": 5, + "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "开始编译教师版本pdf文件: 临时文件/复数向量_教师用_20221016.tex\n", + "开始编译教师版本pdf文件: 临时文件/周末卷05_预选_教师用_20221018.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/复数向量_学生用_20221016.tex\n", + "开始编译学生版本pdf文件: 临时文件/周末卷05_预选_学生用_20221018.tex\n", "0\n" ] } @@ -26,14 +26,14 @@ "\"\"\"---设置题目列表---\"\"\"\n", "#留空为编译全题库, a为读取临时文件中的题号筛选.txt文件生成题库\n", "problems = r\"\"\"\n", - "173,382,1884,1900,1908,1915,1997,2011,2022,2024,2081,2094,3335,3342,3350,3354,3531,3702,3841,4337,4754,7018,7042,7050,7065,7068\n", + "30169,173,182,187,298,1677,3531,3533,4092,3891,1643,3455,3462,3495,4180,3500\n", "\n", "\"\"\"\n", "\"\"\"---设置题目列表结束---\"\"\"\n", "\n", "\"\"\"---设置文件名---\"\"\"\n", "#目录和文件的分隔务必用/\n", - "filename = \"临时文件/复数向量\"\n", + "filename = \"临时文件/周末卷05_预选\"\n", "\"\"\"---设置文件名结束---\"\"\"\n", "\n", "\n", @@ -174,7 +174,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, @@ -188,12 +188,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.9.7" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" + "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" } } }, diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 564a9fba..230af540 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -4315,7 +4315,9 @@ "20220624\t王伟叶, 余利成" ], "same": [], - "related": [], + "related": [ + "030169" + ], "remark": "", "space": "12ex" }, @@ -105274,7 +105276,7 @@ }, "004196": { "id": "004196", - "content": "课本中介绍了应用祖暅原理推导棱锥体积公式的做法. 祖暅原理也可用来求旋转体的体积. 现介绍用祖暅原理求球体体积公式的做法: 可构造一个底面半径和高都与球半径相等的圆柱, 然后在圆柱内挖去一个以圆柱下底面圆心为顶点, 圆柱上底面为底面的圆锥, 用这样一个几何体与半球应用祖暅原理(左图), 即可求得球的体积公式. 请研究和理解球的体积公式求法的基础上, 解答以下问题: 已知椭圆的标准方程为$\\dfrac{x^2}4+\\dfrac{y^2}{25}=1$, 将此椭圆绕$y$轴旋转一周后, 得一橄榄状的几何体(右图), 其体积等于\\blank{50}.\n\\begin{center}\n \\begin{tikzpicture}\n \\draw (0,0) arc (180:0:2) arc (0:-180:2 and 0.5);\n \\draw [dashed] (0,0) arc (180:0:2 and 0.5) -- (0,0);\n \\fill [color = gray!30] (2,1) ellipse ({sqrt(3)} and {sqrt(3)/4});\n \\draw ({2-sqrt(3)},{1}) arc (180:360:{sqrt(3)} and {sqrt(3)/4});\n \\draw [dashed] ({2-sqrt(3)},{1}) arc (180:0:{sqrt(3)} and {sqrt(3)/4});\n \\draw [dashed] (2,0) -- (2,1) (2,0.2) node [left] {$h$};\n \\draw [dashed] (2,0) -- ({2+sqrt(3)},1) (3,0) node [below] {$R$};\n \\filldraw [even odd rule, gray!30] (7,1) ellipse (2 and 0.5) (7,1) ellipse (1 and 0.25);\n \\draw (5,0) arc (180:360:2 and 0.5) (5,2) arc (180:-180:2 and 0.5) (5,0) -- (5,2) (9,0) -- (9,2);\n \\draw [dashed] (5,0) -- (9,0) (7,0) -- (7,1) (7,0) -- (5,2) (7,0) -- (9,2) (8,0) node [below] {$R$} (7,0.4) node [left] {$h$};\n \\draw (5,1) arc (180:360:2 and 0.5);\n \\draw [dashed] (5,1) arc (180:0:2 and 0.5) (6,1) arc (180:-180:1 and 0.25);\n \\end{tikzpicture}\n \\begin{tikzpicture}{>=latex}\n \\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n \\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n \\draw (0,0) node [below left] {$O$};\n \\draw (0,0) ellipse (1 and 1.5);\n \\draw [dashed] (0,0) ellipse (0.5 and 1.5);\n \\end{tikzpicture}\n\\end{center}", + "content": "课本中介绍了应用祖暅原理推导棱锥体积公式的做法. 祖暅原理也可用来求旋转体的体积. 现介绍用祖暅原理求球体体积公式的做法: 可构造一个底面半径和高都与球半径相等的圆柱, 然后在圆柱内挖去一个以圆柱下底面圆心为顶点, 圆柱上底面为底面的圆锥, 用这样一个几何体与半球应用祖暅原理(左图), 即可求得球的体积公式. 请研究和理解球的体积公式求法的基础上, 解答以下问题: 已知椭圆的标准方程为$\\dfrac{x^2}4+\\dfrac{y^2}{25}=1$, 将此椭圆绕$y$轴旋转一周后, 得一橄榄状的几何体(右图), 其体积等于\\blank{50}.\n\\begin{center}\n \\begin{tikzpicture}\n \\draw (0,0) arc (180:0:2) arc (0:-180:2 and 0.5);\n \\draw [dashed] (0,0) arc (180:0:2 and 0.5) -- (0,0);\n \\fill [color = gray!30] (2,1) ellipse ({sqrt(3)} and {sqrt(3)/4});\n \\draw ({2-sqrt(3)},{1}) arc (180:360:{sqrt(3)} and {sqrt(3)/4});\n \\draw [dashed] ({2-sqrt(3)},{1}) arc (180:0:{sqrt(3)} and {sqrt(3)/4});\n \\draw [dashed] (2,0) -- (2,1) (2,0.2) node [left] {$h$};\n \\draw [dashed] (2,0) -- ({2+sqrt(3)},1) (3,0) node [below] {$R$};\n \\filldraw [even odd rule, gray!30] (7,1) ellipse (2 and 0.5) (7,1) ellipse (1 and 0.25);\n \\draw (5,0) arc (180:360:2 and 0.5) (5,2) arc (180:-180:2 and 0.5) (5,0) -- (5,2) (9,0) -- (9,2);\n \\draw [dashed] (5,0) -- (9,0) (7,0) -- (7,1) (7,0) -- (5,2) (7,0) -- (9,2) (8,0) node [below] {$R$} (7,0.4) node [left] {$h$};\n \\draw (5,1) arc (180:360:2 and 0.5);\n \\draw [dashed] (5,1) arc (180:0:2 and 0.5) (6,1) arc (180:-180:1 and 0.25);\n \\end{tikzpicture}\n \\begin{tikzpicture}[>=latex]\n \\draw [->] (-1.5,0) -- (1.5,0) node [below] {$x$};\n \\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n \\draw (0,0) node [below left] {$O$};\n \\draw (0,0) ellipse (1 and 1.5);\n \\draw [dashed] (0,0) ellipse (0.5 and 1.5);\n \\end{tikzpicture}\n\\end{center}", "objs": [ "K0616001B", "K0623001B" @@ -231497,7 +231499,7 @@ }, "009693": { "id": "009693", - "content": "如图, 平面$\\alpha$上的斜线$l$与平面$\\alpha$所成的角为$\\theta$, $l'$是$l$在平面$\\alpha$上的投影, $O$是$l$与平面$\\alpha$的交点, 点$B$是$l$上一点$A$在$\\alpha$上的投影, $OC$是$\\alpha$上的任意一条直线. 如果$\\theta =45^\\circ$, $\\angle BOC=45^\\circ$, 求$\\angle AOC$, 并验证$\\angle AOC>\\theta$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (-1,0,0) -- (3,0,0) node [right] {$l'$} (2,2,0) node [above] {$A$} coordinate (A) -- (2,0,0) coordinate (B) node [below] {$B$} (2.5,2.5,0) node [right] {$l$} -- (0,0,0) coordinate (O) node [below] {$O$};\n\\draw (1,0,1) node [below] {$C$} coordinate (C);\n\\draw ($(O)!-0.5!(C)$) -- ($(O)!1.8!(C)$) node [right] {$l''$};\n\\draw [name path = edge] (-1.5,0,-2.5) coordinate (L) -- (-1.5,0,2.5) --++ (5,0,0) --++ (0,0,-5) coordinate (R);\n\\path [name path = LR] (L) -- (R);\n\\path [name path = OA] (O) -- (A);\n\\path [name path = AB] (A) -- (B);\n\\path [name intersections = {of = OA and LR, by = A1}];\n\\path [name intersections = {of = AB and LR, by = B1}];\n\\draw (L) -- (A1) (B1) -- (R);\n\\draw [dashed] (A1) -- (B1);\n\\path [name path = down] ($(O)!-0.6!(A)$) -- (O);\n\\path [name intersections = {of = down and edge, by = T}];\n\\draw (T) -- ($(O)!-0.6!(A)$);\n\\draw [dashed] (T) -- (O);\n\\draw (O) pic [\"$\\theta$\",draw,angle eccentricity = 1.5] {angle = B--O--A};\n\\draw (O) pic [\"$45^\\circ$\",scale = 1.1,draw,angle eccentricity = 1.7]{angle = C--O--B};\n\\end{tikzpicture}\n\\end{center}", + "content": "如图, 平面$\\alpha$上的斜线$l$与平面$\\alpha$所成的角为$\\theta$, $l'$是$l$在平面$\\alpha$上的投影, $O$是$l$与平面$\\alpha$的交点, 点$B$是$l$上一点$A$在$\\alpha$上的投影, $OC$是$\\alpha$上的任意一条与$l'$不重合的直线. 如果$\\theta =45^\\circ$, $\\angle BOC=45^\\circ$, 求$\\angle AOC$, 并验证$\\angle AOC>\\theta$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (-1,0,0) -- (3,0,0) node [right] {$l'$} (2,2,0) node [above] {$A$} coordinate (A) -- (2,0,0) coordinate (B) node [below] {$B$} (2.5,2.5,0) node [right] {$l$} -- (0,0,0) coordinate (O) node [below] {$O$};\n\\draw (1,0,1) node [below] {$C$} coordinate (C);\n\\draw ($(O)!-0.5!(C)$) -- ($(O)!1.8!(C)$) node [right] {$l''$};\n\\draw [name path = edge] (-1.5,0,-2.5) coordinate (L) -- (-1.5,0,2.5) --++ (5,0,0) --++ (0,0,-5) coordinate (R);\n\\path [name path = LR] (L) -- (R);\n\\path [name path = OA] (O) -- (A);\n\\path [name path = AB] (A) -- (B);\n\\path [name intersections = {of = OA and LR, by = A1}];\n\\path [name intersections = {of = AB and LR, by = B1}];\n\\draw (L) -- (A1) (B1) -- (R);\n\\draw [dashed] (A1) -- (B1);\n\\path [name path = down] ($(O)!-0.6!(A)$) -- (O);\n\\path [name intersections = {of = down and edge, by = T}];\n\\draw (T) -- ($(O)!-0.6!(A)$);\n\\draw [dashed] (T) -- (O);\n\\draw (O) pic [\"$\\theta$\",draw,angle eccentricity = 1.5] {angle = B--O--A};\n\\draw (O) pic [\"$45^\\circ$\",scale = 1.1,draw,angle eccentricity = 1.7]{angle = C--O--B};\n\\end{tikzpicture}\n\\end{center}", "objs": [ "K0610005B" ], @@ -292658,5 +292660,32 @@ ], "remark": "", "space": "" + }, + "030169": { + "id": "030169", + "content": "已知复数$z=\\dfrac{(-3-\\mathrm{\\mathrm{i}})^2(2-\\mathrm{\\mathrm{i}})}{(1+2\\mathrm{i})^3}$, 则$|z|=$\\blank{50}.", + "objs": [ + "K0514004B", + "K0514001B" + ], + "tags": [ + "第五单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "教材复习题-20221018修改", + "edit": [ + "20220624\t王伟叶, 余利成", + "20221018\t王伟叶" + ], + "same": [], + "related": [ + "000167" + ], + "remark": "", + "space": "" } } \ No newline at end of file