22 KiB
22 KiB
excalidraw-plugin, tags
| excalidraw-plugin | tags | |
|---|---|---|
| parsed |
|
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠==
Text Elements
e ^i0aQMqP4
1 ^HGGIdYdn
e ^xFSNzZfe
2 ^rXnI70LR
vecteurs verts : rotation d'angle theta ^ZIK9eMYM
sin ^ac2QIp4V
cos ^Geo1ilXi
-sin ^9a6h8pKg
cos ^kMXx02Q0
Embedded files
39f23bfc61b3770886c6aafc962a252806f589ab: r_\theta(e_1) = \begin{pmatrix} \cos \theta\\ \sin\theta \end{pmatrix}
04dce9015e346c50f6d5187637734664de5e4aeb: r_\theta(e_2) = \begin{pmatrix} -\sin \theta\\ \cos\theta \end{pmatrix}
304851cecddcd1fb7edb8f187e999c2c88676f0e: r_\theta \widehat{=} \begin{pmatrix} \cos\theta & -\sin \theta\\ \sin\theta & \cos\theta \end{pmatrix}
%%
Drawing
{
"type": "excalidraw",
"version": 2,
"source": "https://excalidraw.com",
"elements": [
{
"type": "ellipse",
"version": 34,
"versionNonce": 13394162,
"isDeleted": false,
"id": "iYnAwiGSmRkjBWvpETyyy",
"fillStyle": "hachure",
"strokeWidth": 1,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": -10.2734375,
"y": -172.125,
"strokeColor": "#000000",
"backgroundColor": "transparent",
"width": 363.09375,
"height": 363.09375,
"seed": 2085845618,
"groupIds": [],
"strokeSharpness": "sharp",
"boundElements": [],
"updated": 1668014190503,
"link": null,
"locked": false
},
{
"type": "arrow",
"version": 87,
"versionNonce": 974534258,
"isDeleted": false,
"id": "ycUuTKXUp7kVLnhSHwwQo",
"fillStyle": "hachure",
"strokeWidth": 1,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 174.62890625,
"y": 9.665226485077412,
"strokeColor": "#000000",
"backgroundColor": "transparent",
"width": 176.62969309815207,
"height": 0,
"seed": 213852014,
"groupIds": [],
"strokeSharpness": "round",
"boundElements": [],
"updated": 1668014169551,
"link": null,
"locked": false,
"startBinding": null,
"endBinding": null,
"lastCommittedPoint": null,
"startArrowhead": null,
"endArrowhead": "triangle",
"points": [
[
0,
0
],
[
176.62969309815207,
0
]
]
},
{
"type": "arrow",
"version": 82,
"versionNonce": 866079922,
"isDeleted": false,
"id": "Z28dKVhlE3NfR1A8Iaz9l",
"fillStyle": "hachure",
"strokeWidth": 1,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 171.5362235539049,
"y": 11.184087130827834,
"strokeColor": "#000000",
"backgroundColor": "transparent",
"width": 0,
"height": 182.15625,
"seed": 439585714,
"groupIds": [],
"strokeSharpness": "round",
"boundElements": [],
"updated": 1668014179870,
"link": null,
"locked": false,
"startBinding": null,
"endBinding": {
"elementId": "rXnI70LR",
"focus": 1.8187142432618872,
"gap": 7.836430880827834
},
"lastCommittedPoint": null,
"startArrowhead": null,
"endArrowhead": "triangle",
"points": [
[
0,
0
],
[
0,
-182.15625
]
]
},
{
"type": "text",
"version": 9,
"versionNonce": 519466354,
"isDeleted": false,
"id": "i0aQMqP4",
"fillStyle": "hachure",
"strokeWidth": 1,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 379,
"y": 0.7890625,
"strokeColor": "#000000",
"backgroundColor": "transparent",
"width": 18,
"height": 36,
"seed": 1811369262,
"groupIds": [
"HKZjkv_Jh_yBNyx9qfx8D"
],
"strokeSharpness": "sharp",
"boundElements": [],
"updated": 1668014170792,
"link": null,
"locked": false,
"fontSize": 28,
"fontFamily": 1,
"text": "e",
"rawText": "e",
"baseline": 25,
"textAlign": "left",
"verticalAlign": "top",
"containerId": null,
"originalText": "e"
},
{
"type": "text",
"version": 24,
"versionNonce": 1141299886,
"isDeleted": false,
"id": "HGGIdYdn",
"fillStyle": "hachure",
"strokeWidth": 1,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 395.171875,
"y": 24.4296875,
"strokeColor": "#000000",
"backgroundColor": "transparent",
"width": 8,
"height": 25,
"seed": 84997102,
"groupIds": [
"HKZjkv_Jh_yBNyx9qfx8D"
],
"strokeSharpness": "sharp",
"boundElements": [],
"updated": 1668014170792,
"link": null,
"locked": false,
"fontSize": 20,
"fontFamily": 1,
"text": "1",
"rawText": "1",
"baseline": 18,
"textAlign": "left",
"verticalAlign": "top",
"containerId": null,
"originalText": "1"
},
{
"type": "text",
"version": 30,
"versionNonce": 2047378162,
"isDeleted": false,
"id": "xFSNzZfe",
"fillStyle": "hachure",
"strokeWidth": 1,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 161.9140625,
"y": -227.44921875,
"strokeColor": "#000000",
"backgroundColor": "transparent",
"width": 18,
"height": 36,
"seed": 2012435694,
"groupIds": [
"6cr8v9FrDOW4RJuu_dZVe"
],
"strokeSharpness": "sharp",
"boundElements": [],
"updated": 1668014179865,
"link": null,
"locked": false,
"fontSize": 28,
"fontFamily": 1,
"text": "e",
"rawText": "e",
"baseline": 25,
"textAlign": "left",
"verticalAlign": "top",
"containerId": null,
"originalText": "e"
},
{
"type": "text",
"version": 47,
"versionNonce": 1479739246,
"isDeleted": false,
"id": "rXnI70LR",
"fillStyle": "hachure",
"strokeWidth": 1,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 178.0859375,
"y": -203.80859375,
"strokeColor": "#000000",
"backgroundColor": "transparent",
"width": 16,
"height": 25,
"seed": 860567794,
"groupIds": [
"6cr8v9FrDOW4RJuu_dZVe"
],
"strokeSharpness": "sharp",
"boundElements": [
{
"id": "Z28dKVhlE3NfR1A8Iaz9l",
"type": "arrow"
}
],
"updated": 1668014179870,
"link": null,
"locked": false,
"fontSize": 20,
"fontFamily": 1,
"text": "2",
"rawText": "2",
"baseline": 18,
"textAlign": "left",
"verticalAlign": "top",
"containerId": null,
"originalText": "2"
},
{
"type": "arrow",
"version": 192,
"versionNonce": 1035941550,
"isDeleted": false,
"id": "amgMXRxHfZXEoHtEMYyNx",
"fillStyle": "hachure",
"strokeWidth": 1,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 173.65625,
"y": 7.11328125,
"strokeColor": "#5c940d",
"backgroundColor": "transparent",
"width": 157.14453125,
"height": 76.6484375,
"seed": 930867630,
"groupIds": [],
"strokeSharpness": "round",
"boundElements": [],
"updated": 1668014234514,
"link": null,
"locked": false,
"startBinding": null,
"endBinding": null,
"lastCommittedPoint": null,
"startArrowhead": null,
"endArrowhead": "triangle",
"points": [
[
0,
0
],
[
157.14453125,
-76.6484375
]
]
},
{
"type": "text",
"version": 145,
"versionNonce": 1457401390,
"isDeleted": false,
"id": "ZIK9eMYM",
"fillStyle": "hachure",
"strokeWidth": 1,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 254.91174768518522,
"y": -224.09071180555554,
"strokeColor": "#5c940d",
"backgroundColor": "transparent",
"width": 397,
"height": 25,
"seed": 661181550,
"groupIds": [],
"strokeSharpness": "sharp",
"boundElements": [],
"updated": 1668014695646,
"link": null,
"locked": false,
"fontSize": 20,
"fontFamily": 1,
"text": "vecteurs verts : rotation d'angle theta",
"rawText": "vecteurs verts : rotation d'angle theta",
"baseline": 18,
"textAlign": "left",
"verticalAlign": "top",
"containerId": null,
"originalText": "vecteurs verts : rotation d'angle theta"
},
{
"type": "arrow",
"version": 138,
"versionNonce": 402862638,
"isDeleted": false,
"id": "rnh1nM61w7V5I35zfeXcF",
"fillStyle": "hachure",
"strokeWidth": 1,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 172.35546875,
"y": 9.2421875,
"strokeColor": "#5c940d",
"backgroundColor": "transparent",
"width": 81.08984375,
"height": 156.6015625,
"seed": 1064558254,
"groupIds": [],
"strokeSharpness": "round",
"boundElements": [],
"updated": 1668014250456,
"link": null,
"locked": false,
"startBinding": null,
"endBinding": null,
"lastCommittedPoint": null,
"startArrowhead": null,
"endArrowhead": "triangle",
"points": [
[
0,
0
],
[
-81.08984375,
-156.6015625
]
]
},
{
"type": "line",
"version": 59,
"versionNonce": 1462204978,
"isDeleted": false,
"id": "FtiPL5iFnhMHuXJ9Vm2fV",
"fillStyle": "hachure",
"strokeWidth": 4,
"strokeStyle": "dotted",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 332.6640625,
"y": -68.05078125,
"strokeColor": "#1864ab",
"backgroundColor": "transparent",
"width": 0,
"height": 78.8046875,
"seed": 365567218,
"groupIds": [],
"strokeSharpness": "round",
"boundElements": [],
"updated": 1668014330477,
"link": null,
"locked": false,
"startBinding": null,
"endBinding": null,
"lastCommittedPoint": null,
"startArrowhead": null,
"endArrowhead": null,
"points": [
[
0,
0
],
[
0,
78.8046875
]
]
},
{
"type": "line",
"version": 76,
"versionNonce": 1972875122,
"isDeleted": false,
"id": "0UxQsbLZbxiu9gAaMeYez",
"fillStyle": "hachure",
"strokeWidth": 4,
"strokeStyle": "dotted",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 93.57421875,
"y": -149.2109375,
"strokeColor": "#c92a2a",
"backgroundColor": "transparent",
"width": 75.6484375,
"height": 0,
"seed": 1078132398,
"groupIds": [],
"strokeSharpness": "round",
"boundElements": [],
"updated": 1668014270595,
"link": null,
"locked": false,
"startBinding": null,
"endBinding": null,
"lastCommittedPoint": null,
"startArrowhead": null,
"endArrowhead": null,
"points": [
[
0,
0
],
[
75.6484375,
0
]
]
},
{
"type": "line",
"version": 72,
"versionNonce": 1149876654,
"isDeleted": false,
"id": "3tQM4ReM4zrUQSjjOs451",
"fillStyle": "hachure",
"strokeWidth": 4,
"strokeStyle": "dotted",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 91.9140625,
"y": -145.4375,
"strokeColor": "#1864ab",
"backgroundColor": "transparent",
"width": 1.4210854715202004e-14,
"height": 156.09375,
"seed": 1033171250,
"groupIds": [],
"strokeSharpness": "round",
"boundElements": [],
"updated": 1668014280720,
"link": null,
"locked": false,
"startBinding": null,
"endBinding": null,
"lastCommittedPoint": null,
"startArrowhead": null,
"endArrowhead": null,
"points": [
[
0,
0
],
[
-1.4210854715202004e-14,
156.09375
]
]
},
{
"type": "line",
"version": 71,
"versionNonce": 1863712434,
"isDeleted": false,
"id": "O6m4MtQfkEeJmUWyK9ZTl",
"fillStyle": "hachure",
"strokeWidth": 4,
"strokeStyle": "dotted",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 331.28125,
"y": -70.3828125,
"strokeColor": "#c92a2a",
"backgroundColor": "transparent",
"width": 157.26171875,
"height": 0,
"seed": 3123698,
"groupIds": [],
"strokeSharpness": "round",
"boundElements": [],
"updated": 1668014324478,
"link": null,
"locked": false,
"startBinding": null,
"endBinding": null,
"lastCommittedPoint": null,
"startArrowhead": null,
"endArrowhead": null,
"points": [
[
0,
0
],
[
-157.26171875,
0
]
]
},
{
"type": "line",
"version": 97,
"versionNonce": 877919598,
"isDeleted": false,
"id": "QyOYoLv6qB7D1QKHWrq6u",
"fillStyle": "hachure",
"strokeWidth": 4,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 175.41796875,
"y": 10.45703125,
"strokeColor": "#c92a2a",
"backgroundColor": "transparent",
"width": 157.3046875,
"height": 0,
"seed": 1685370094,
"groupIds": [],
"strokeSharpness": "round",
"boundElements": [],
"updated": 1668014324478,
"link": null,
"locked": false,
"startBinding": null,
"endBinding": null,
"lastCommittedPoint": null,
"startArrowhead": null,
"endArrowhead": null,
"points": [
[
0,
0
],
[
157.3046875,
0
]
]
},
{
"type": "text",
"version": 256,
"versionNonce": 2123937714,
"isDeleted": false,
"id": "ac2QIp4V",
"fillStyle": "hachure",
"strokeWidth": 4,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 132.828125,
"y": -98.0078125,
"strokeColor": "#1864ab",
"backgroundColor": "transparent",
"width": 37,
"height": 36,
"seed": 1541122606,
"groupIds": [],
"strokeSharpness": "sharp",
"boundElements": [],
"updated": 1668014353898,
"link": null,
"locked": false,
"fontSize": 28,
"fontFamily": 1,
"text": "sin",
"rawText": "sin",
"baseline": 25,
"textAlign": "left",
"verticalAlign": "top",
"containerId": null,
"originalText": "sin"
},
{
"type": "text",
"version": 42,
"versionNonce": 572035058,
"isDeleted": false,
"id": "Geo1ilXi",
"fillStyle": "hachure",
"strokeWidth": 4,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 287.68359375,
"y": 13.38671875,
"strokeColor": "#c92a2a",
"backgroundColor": "transparent",
"width": 47,
"height": 36,
"seed": 1101829806,
"groupIds": [],
"strokeSharpness": "sharp",
"boundElements": [],
"updated": 1668014359563,
"link": null,
"locked": false,
"fontSize": 28,
"fontFamily": 1,
"text": "cos",
"rawText": "cos",
"baseline": 25,
"textAlign": "left",
"verticalAlign": "top",
"containerId": null,
"originalText": "cos"
},
{
"type": "line",
"version": 89,
"versionNonce": 839630514,
"isDeleted": false,
"id": "DTnkPf5ZcVKGzks4xFUU4",
"fillStyle": "hachure",
"strokeWidth": 4,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 170.90234375,
"y": 10.19140625,
"strokeColor": "#5f3dc4",
"backgroundColor": "transparent",
"width": 79.71484375,
"height": 0,
"seed": 1478869426,
"groupIds": [],
"strokeSharpness": "round",
"boundElements": [],
"updated": 1668014377439,
"link": null,
"locked": false,
"startBinding": null,
"endBinding": null,
"lastCommittedPoint": null,
"startArrowhead": null,
"endArrowhead": null,
"points": [
[
0,
0
],
[
-79.71484375,
0
]
]
},
{
"type": "text",
"version": 24,
"versionNonce": 1260422382,
"isDeleted": false,
"id": "9a6h8pKg",
"fillStyle": "hachure",
"strokeWidth": 4,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 58.3203125,
"y": 8.6484375,
"strokeColor": "#5f3dc4",
"backgroundColor": "transparent",
"width": 48,
"height": 36,
"seed": 665664050,
"groupIds": [],
"strokeSharpness": "sharp",
"boundElements": [],
"updated": 1668014387547,
"link": null,
"locked": false,
"fontSize": 28,
"fontFamily": 1,
"text": "-sin",
"rawText": "-sin",
"baseline": 25,
"textAlign": "left",
"verticalAlign": "top",
"containerId": null,
"originalText": "-sin"
},
{
"type": "line",
"version": 141,
"versionNonce": 1952428590,
"isDeleted": false,
"id": "wO2c1K6mgS8YC78Z7o96C",
"fillStyle": "hachure",
"strokeWidth": 4,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 171.13303083737196,
"y": 10.2578125,
"strokeColor": "#c92a2a",
"backgroundColor": "transparent",
"width": 0,
"height": 158.38671875,
"seed": 987608878,
"groupIds": [],
"strokeSharpness": "round",
"boundElements": [],
"updated": 1668014413097,
"link": null,
"locked": false,
"startBinding": null,
"endBinding": null,
"lastCommittedPoint": null,
"startArrowhead": null,
"endArrowhead": null,
"points": [
[
0,
0
],
[
0,
-158.38671875
]
]
},
{
"type": "line",
"version": 107,
"versionNonce": 1768672622,
"isDeleted": false,
"id": "XgAQFhs8jMIaP6_JR6W_R",
"fillStyle": "hachure",
"strokeWidth": 4,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 170.35546875,
"y": -67.73321404950433,
"strokeColor": "#1864ab",
"backgroundColor": "transparent",
"width": 0,
"height": 77.56640625000001,
"seed": 1482515442,
"groupIds": [],
"strokeSharpness": "round",
"boundElements": [],
"updated": 1668014407978,
"link": null,
"locked": false,
"startBinding": null,
"endBinding": null,
"lastCommittedPoint": null,
"startArrowhead": null,
"endArrowhead": null,
"points": [
[
0,
0
],
[
0,
77.56640625000001
]
]
},
{
"type": "text",
"version": 26,
"versionNonce": 1883748850,
"isDeleted": false,
"id": "kMXx02Q0",
"fillStyle": "hachure",
"strokeWidth": 4,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 178.7221924692051,
"y": -165.89762382214857,
"strokeColor": "#c92a2a",
"backgroundColor": "transparent",
"width": 47,
"height": 36,
"seed": 260013742,
"groupIds": [],
"strokeSharpness": "sharp",
"boundElements": [],
"updated": 1668014417814,
"link": null,
"locked": false,
"fontSize": 28,
"fontFamily": 1,
"text": "cos",
"rawText": "cos",
"baseline": 25,
"textAlign": "left",
"verticalAlign": "top",
"containerId": null,
"originalText": "cos"
},
{
"type": "image",
"version": 45,
"versionNonce": 932586930,
"isDeleted": false,
"id": "kqwmvrUH",
"fillStyle": "hachure",
"strokeWidth": 1,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 447.623139849123,
"y": -163.08240928704294,
"strokeColor": "#000000",
"backgroundColor": "transparent",
"width": 133,
"height": 43,
"seed": 26563,
"groupIds": [],
"strokeSharpness": "sharp",
"boundElements": [],
"updated": 1668014497978,
"link": null,
"locked": false,
"status": "pending",
"fileId": "39f23bfc61b3770886c6aafc962a252806f589ab",
"scale": [
1,
1
]
},
{
"type": "image",
"version": 102,
"versionNonce": 1332837422,
"isDeleted": false,
"id": "jUGxd0j5",
"fillStyle": "hachure",
"strokeWidth": 1,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 432.6231398491229,
"y": -85.87299401785356,
"strokeColor": "#000000",
"backgroundColor": "transparent",
"width": 148,
"height": 43,
"seed": 81906,
"groupIds": [],
"strokeSharpness": "sharp",
"boundElements": [],
"updated": 1668014493505,
"link": null,
"locked": false,
"status": "pending",
"fileId": "04dce9015e346c50f6d5187637734664de5e4aeb",
"scale": [
1,
1
]
},
{
"type": "line",
"version": 291,
"versionNonce": 1862017006,
"isDeleted": false,
"id": "X6FVgAFGjb10hlIZpB8Wp",
"fillStyle": "hachure",
"strokeWidth": 1,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 580.88565521667,
"y": -170.81326604811017,
"strokeColor": "#000000",
"backgroundColor": "transparent",
"width": 29.628734754485095,
"height": 144.49355587370889,
"seed": 485138290,
"groupIds": [],
"strokeSharpness": "round",
"boundElements": [],
"updated": 1668014525130,
"link": null,
"locked": false,
"startBinding": null,
"endBinding": null,
"lastCommittedPoint": null,
"startArrowhead": null,
"endArrowhead": null,
"points": [
[
0,
0
],
[
10.807023218481845,
8.57065656402142
],
[
14.233411793821347,
69.73653393035937
],
[
29.628734754485095,
78.56643411493974
],
[
15.676430501028904,
85.32863216927882
],
[
15.857588693708749,
136.877508238014
],
[
3.6421645008454107,
144.49355587370889
]
]
},
{
"type": "image",
"version": 136,
"versionNonce": 1735071410,
"isDeleted": false,
"id": "y947MRoh",
"fillStyle": "hachure",
"strokeWidth": 1,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"angle": 0,
"x": 625.4593981999676,
"y": -113.991101129886,
"strokeColor": "#000000",
"backgroundColor": "transparent",
"width": 164,
"height": 43,
"seed": 74768,
"groupIds": [],
"strokeSharpness": "sharp",
"boundElements": [],
"updated": 1668014643964,
"link": null,
"locked": false,
"status": "pending",
"fileId": "304851cecddcd1fb7edb8f187e999c2c88676f0e",
"scale": [
1,
1
]
}
],
"appState": {
"theme": "dark",
"viewBackgroundColor": "#ffffff",
"currentItemStrokeColor": "#000000",
"currentItemBackgroundColor": "transparent",
"currentItemFillStyle": "hachure",
"currentItemStrokeWidth": 1,
"currentItemStrokeStyle": "solid",
"currentItemRoughness": 1,
"currentItemOpacity": 100,
"currentItemFontFamily": 1,
"currentItemFontSize": 20,
"currentItemTextAlign": "left",
"currentItemStrokeSharpness": "sharp",
"currentItemStartArrowhead": null,
"currentItemEndArrowhead": "triangle",
"currentItemLinearStrokeSharpness": "round",
"gridSize": null,
"colorPalette": {}
},
"files": {}
}
%%