录入24届赋能补充题至8B

题库0.3/Problems.json

@@ -617432,6 +617432,106 @@
         "space": "",
         "unrelated": []
     },
+    "023041": {
+        "id": "023041",
+        "content": "已知向量 $\\overrightarrow{AB}=(1,2)$, $\\overrightarrow{AC}=(3,5)$, 则向量 $\\overrightarrow{BC}$ 的坐标是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "24届赋能补充题目",
+        "edit": [
+            "20240105\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023042": {
+        "id": "023042",
+        "content": "在二项式 $(x^2-\\dfrac{1}{x})^5$ 的展开式中, $x^4$ 项的系数为\\blank{50}. (结果用数值表示)",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "24届赋能补充题目",
+        "edit": [
+            "20240105\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023043": {
+        "id": "023043",
+        "content": "若 $\\alpha$、$\\beta$ 是一元二次方程 $2 x^2+x+3=0$ 的两个根, 则 $\\dfrac{1}{\\alpha}+\\dfrac{1}{\\beta}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "24届赋能补充题目",
+        "edit": [
+            "20240105\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023044": {
+        "id": "023044",
+        "content": "在 $\\triangle ABC$ 中, 内角 $A, B, C$ 的对边是 $a, b, c$. 若 $a^2=(2+\\sqrt{3}) b^2$, $b=c$, 则 $A=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "24届赋能补充题目",
+        "edit": [
+            "20240105\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023045": {
+        "id": "023045",
+        "content": "给定空间中的直线 $l$ 及平面 $\\alpha$, 则条件``直线 $l$ 与平面 $\\alpha$ 内无数条直线都垂直''是``直线 $l$与平面 $\\alpha$ 垂直''的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分也非必要条件}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "24届赋能补充题目",
+        "edit": [
+            "20240105\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "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) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",