diff --git a/工具v2/文本文件/新题收录列表.txt b/工具v2/文本文件/新题收录列表.txt index 975614ea..806ff422 100644 --- a/工具v2/文本文件/新题收录列表.txt +++ b/工具v2/文本文件/新题收录列表.txt @@ -88,3 +88,6 @@ 20240125-113548 023848:023855 +20240125-113926 +023856:023864 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 977a562a..d56ef886 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -26143,7 +26143,9 @@ "20220624\t朱敏慧, 王伟叶" ], "same": [], - "related": [], + "related": [ + "023858" + ], "remark": "", "space": "", "unrelated": [] @@ -61720,7 +61722,9 @@ "20220625\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023860" + ], "remark": "", "space": "", "unrelated": [] @@ -67389,7 +67393,9 @@ "20220625\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023862" + ], "remark": "", "space": "", "unrelated": [] @@ -69886,7 +69892,9 @@ "20220625\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023857" + ], "remark": "", "space": "", "unrelated": [] @@ -247624,7 +247632,9 @@ "20220726\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023857" + ], "remark": "", "space": "4em", "unrelated": [] @@ -398989,7 +398999,9 @@ "20230202\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023856" + ], "remark": "", "space": "4em", "unrelated": [] @@ -643640,6 +643652,198 @@ "space": "4em", "unrelated": [] }, + "023856": { + "id": "023856", + "content": "设向量 $\\overrightarrow{a}=(3,2)$, $\\overrightarrow{b}=(1,-4)$, 则 $\\overrightarrow{b}$ 在 $\\overrightarrow{a}$ 方向上的数量投影为\\blank{50}, 投影为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "014337" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023857": { + "id": "023857", + "content": "已知点 $A(8,-1)$、$B(1,-3)$, 若点 $C(2 m-1, m+2)$ 在直线 $AB$ 上, 则实数 $m=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "008761", + "002149" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023858": { + "id": "023858", + "content": "设向量 $\\overrightarrow{p}=(2,7)$, $\\overrightarrow{q}=(x,-3)$. 若 $\\overrightarrow{p}$ 与 $\\overrightarrow{q}$ 的夹角为钝角, 则 $x$ 的取值范围是\\blank{50}, 若 $\\overrightarrow{p}$ 与 $\\overrightarrow{q}$ 的夹角为锐角, 则 $x$ 的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "000699", + "040747" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023859": { + "id": "023859", + "content": "已知 $|\\overrightarrow{a}|=5$, $|\\overrightarrow{b}|=8, \\overrightarrow{a}$ 与 $\\overrightarrow{b}$ 的夹角为 $60^{\\circ}$, 则 $|\\overrightarrow{a}+\\overrightarrow{b}|=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023860": { + "id": "023860", + "content": "设 $\\overrightarrow{a}=(m+1,-3)$, $\\overrightarrow{b}=(1, m-1)$, 且 $\\overrightarrow{a}+\\overrightarrow{b}$ 与 $\\overrightarrow{a}-\\overrightarrow{b}$ 垂直, 则实数 $m=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "001891" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023861": { + "id": "023861", + "content": "若 $|\\overrightarrow{a}|=3$, $|\\overrightarrow{b}|=4$, $(\\overrightarrow{a}+2 \\overrightarrow{b}) \\cdot(2 \\overrightarrow{a}-\\overrightarrow{b})=-32$, 则 $\\overrightarrow{a}$ 与 $\\overrightarrow{b}$ 的夹角为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023862": { + "id": "023862", + "content": "若将向量 $\\overrightarrow{a}=(3,4)$ 绕原点按逆时针方向旋转 $45^{\\circ}$ 得到向量 $\\overrightarrow{b}$, 则 $\\overrightarrow{b}$ 的坐标为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "002062" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "023863": { + "id": "023863", + "content": "已知 $O$ 为坐标原点, $\\overrightarrow{OA}=(2,2)$, $\\overrightarrow{OB}=(4,1)$, 点 $P$ 在 $x$ 轴上, 则 $\\overrightarrow{AP}\\cdot \\overrightarrow{BP}$ 最小值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023864": { + "id": "023864", + "content": "在平面直角坐标系 $x O y$ 中, 点 $A(-1,-2)$、$B(2,3)$、$C(-2,-1)$.\\\\\n(1) 求以线段 $AB$、$AC$ 为邻边的平行四边形两条对角线的长;\\\\\n(2) 设实数 $t$ 满足 $(\\overrightarrow{AB}-t \\overrightarrow{OC}) \\cdot \\overrightarrow{OC}=0$, 求实数 $t$ 的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, "030001": { "id": "030001", "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0