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diff --git a/.doctrees/assets/index.doctree b/.doctrees/assets/index.doctree
diff --git a/.doctrees/assets/notes/algebra/algebra_2023.11.07.doctree b/.doctrees/assets/notes/algebra/algebra_2023.11.07.doctree
diff --git a/.doctrees/assets/notes/algebra/algebra_2023.11.14.doctree b/.doctrees/assets/notes/algebra/algebra_2023.11.14.doctree
diff --git a/.doctrees/assets/notes/algebra/algebra_2023.11.28.2023.doctree b/.doctrees/assets/notes/algebra/algebra_2023.11.28.2023.doctree
diff --git a/.doctrees/assets/notes/matematyka/matematyka_2023.11.20.doctree b/.doctrees/assets/notes/matematyka/matematyka_2023.11.20.doctree
diff --git a/.doctrees/assets/notes/matematyka/matematyka_2023.11.21.doctree b/.doctrees/assets/notes/matematyka/matematyka_2023.11.21.doctree
diff --git a/.doctrees/assets/notes/mechanika_cw/mechanika_cw_24.11.2023.doctree b/.doctrees/assets/notes/mechanika_cw/mechanika_cw_24.11.2023.doctree
diff --git a/.doctrees/environment.pickle b/.doctrees/environment.pickle
diff --git a/assets/index.html b/assets/index.html
diff --git a/assets/notes/algebra/algebra_2023.11.07.html b/assets/notes/algebra/algebra_2023.11.07.html
@@ -20,6 +20,8 @@
     <script src="../../../_static/translations.js?v=a186e9ce"></script>
     <script src="../../../_static/sphinxcontrib-images/LightBox2/lightbox2/dist/js/lightbox-plus-jquery.min.js?v=ffc8af2d"></script>
     <script src="../../../_static/sphinxcontrib-images/LightBox2/lightbox2-customize/jquery-noconflict.js?v=12818e64"></script>
+    <script>window.MathJax = {"options": {"processHtmlClass": "tex2jax_process|mathjax_process|math|output_area"}}</script>
+    <script defer="defer" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
 
 
 
@@ -64,13 +66,22 @@ <h3>Nawigacja</h3>
 
   <section id="przestrzenie-wektorowe">
 <h1>Przestrzenie wektorowe<a class="headerlink" href="#przestrzenie-wektorowe" title="Link to this heading">¶</a></h1>
-<div class="admonition-definicja admonition">
-<p class="admonition-title">definicja</p>
+<div class="admonition-przestrzen-wektorowa admonition">
+<p class="admonition-title">Przestrzeń Wektorowa</p>
+<p>(K, +, <span class="math notranslate nohighlight">\(*\)</span>) jest grupą abelową, natomiast <code class="docutils literal notranslate"><span class="pre">V</span></code> zbiorem (<span class="math notranslate nohighlight">\(V \neq \emptyset\)</span>).</p>
 <ul class="simple">
 <li><p>(V, +) jest grupą abelową</p></li>
+<li><p><span class="math notranslate nohighlight">\(\forall v, v \in V \quad \forall \alpha \in K \quad \alpha * (v + v) = (\alpha * v) + (\alpha * v)\)</span> (występuje rozdzielność mnożenia względem dodawania w mnożeniu <strong>sumy wektorów</strong> przez <strong>skalar</strong>)</p></li>
+<li><p><span class="math notranslate nohighlight">\(\forall v \in V \quad \forall \alpha, \beta \in K \quad (\alpha + \beta) * v = (\alpha * v) + (\beta * v)\)</span> (występuje rozdzielność mnożenia względem dodawania w mnożenia <strong>sumy skalarów</strong> przez <strong>wektor</strong>)</p></li>
+<li><p><span class="math notranslate nohighlight">\(\forall v \in V \quad \forall \alpha, \beta \in K \quad \alpha * (\beta * v) = (\alpha * \beta) * v\)</span> (mnożenie wektora i skalarów jest łączne)</p></li>
+<li><p><span class="math notranslate nohighlight">\(\forall v \in V \quad 1 * v = v\)</span> (występuje element neutralny)</p></li>
 <li><p>możliwe jest mnożenie przez skalar</p></li>
 </ul>
 </div>
+<div class="admonition tip">
+<p class="admonition-title">Wskazówka</p>
+<p>Elementy zbioru V nazywamy wektorami, a K - skalarami</p>
+</div>
 </section>
 
 

diff --git a/assets/notes/algebra/algebra_2023.11.14.html b/assets/notes/algebra/algebra_2023.11.14.html
@@ -97,7 +97,7 @@ <h3>Nawigacja</h3>
 </div>
 <div class="admonition note">
 <p class="admonition-title">Informacja</p>
-<p>wektory generują przestrzeń <span class="math notranslate nohighlight">\(\mathbb{R}^n \Leftrigharrow\)</span> rząd macierzy złożonej
+<p>wektory generują przestrzeń <span class="math notranslate nohighlight">\(\mathbb{R}^n \Leftrightarrow\)</span> rząd macierzy złożonej
 z tych wektorów jes trówny <code class="docutils literal notranslate"><span class="pre">n</span></code></p>
 </div>
 <section id="baza">

diff --git a/assets/notes/algebra/algebra_2023.11.28.2023.html b/assets/notes/algebra/algebra_2023.11.28.2023.html
@@ -0,0 +1,146 @@
+
+
+<!DOCTYPE html>
+
+<html lang="pl" data-content_root="../../../">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="viewport" content="width=device-width, initial-scale=1" />
+
+    <title>&lt;no title&gt; &#8212; Matematyka  - dokumentacja</title>
+    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/cloud.css?v=f9ae72be" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/sphinxcontrib-images/LightBox2/lightbox2/dist/css/lightbox.css?v=5c84f910" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=6897fae6" />
+    <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noticia+Text:400,i,b,bi|Open+Sans:400,i,b,bi|Roboto+Mono:400,i,b,bi&amp;display=swap" type="text/css" />
+
+    <script src="../../../_static/documentation_options.js?v=a28d12eb"></script>
+    <script src="../../../_static/doctools.js?v=888ff710"></script>
+    <script src="../../../_static/sphinx_highlight.js?v=dc90522c"></script>
+    <script src="../../../_static/translations.js?v=a186e9ce"></script>
+    <script src="../../../_static/sphinxcontrib-images/LightBox2/lightbox2/dist/js/lightbox-plus-jquery.min.js?v=ffc8af2d"></script>
+    <script src="../../../_static/sphinxcontrib-images/LightBox2/lightbox2-customize/jquery-noconflict.js?v=12818e64"></script>
+    <script>window.MathJax = {"options": {"processHtmlClass": "tex2jax_process|mathjax_process|math|output_area"}}</script>
+    <script defer="defer" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
+
+
+
+
+        <script src="../../../_static/jquery.cookie.js"></script>
+
+
+
+
+        <script src="../../../_static/cloud.base.js"></script>
+
+
+
+
+        <script src="../../../_static/cloud.js"></script>
+
+
+    <link rel="index" title="Indeks" href="../../../genindex.html" />
+    <link rel="search" title="Szukaj" href="../../../search.html" /> 
+        <meta name="viewport" content="width=device-width, initial-scale=1">
+  </head><body>
+    <div class="relbar-top">
+
+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Nawigacja</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../../../genindex.html" title="Indeks ogólny"
+             accesskey="I">indeks</a></li>
+    <li><a href="../../../index.html">Matematyka  - dokumentacja</a> &#187;</li>
+
+        <li class="nav-item nav-item-this"><a href="">&lt;no title&gt;</a></li> 
+      </ul>
+    </div>
+    </div>
+
+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+
+  <div class="admonition tip">
+<p class="admonition-title">Wskazówka</p>
+<p>Aby obraz wektorów liniowo niezależnych był liniowo niezależny
+odwzorowanie musi być injektywne.</p>
+<p><em>Na przykład rzutowanie <span class="math notranslate nohighlight">\(\mathbb{R}^3\)</span> na płaszczyznę <span class="math notranslate nohighlight">\(OY\)</span></em></p>
+</div>
+<div class="admonition note">
+<p class="admonition-title">Informacja</p>
+<p>macierz reprezentuje odwzorowanie liniowe</p>
+<ul class="simple">
+<li><p>dodawanie macierzy reprezentuje dodawanie odwzorowań</p></li>
+<li><p>natomiast mnożenie macierzy to składanie</p></li>
+</ul>
+</div>
+<div class="admonition-reprezencacja-macierzowa-odwzorowan-liniowych admonition">
+<p class="admonition-title">Reprezencacja macierzowa odwzorowań liniowych</p>
+<p>Macierz której kolumny nsą <strong>obrazami</strong> wektorów bazowych nazywamy
+reprezentacją macierzową odwzoorowania liniowego</p>
+</div>
+
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper">
+<div id="searchbox" style="display: none" role="search">
+  <h3 id="searchlabel">Szybkie wyszukiwanie</h3>
+    <div class="searchformwrapper">
+    <form class="search" action="../../../search.html" method="get">
+      <input type="text" name="q" aria-labelledby="searchlabel" autocomplete="off" autocorrect="off" autocapitalize="off" spellcheck="false"/>
+      <input type="submit" value="Szukaj" />
+    </form>
+    </div>
+</div>
+<script>document.getElementById('searchbox').style.display = "block"</script>
+        </div>
+      </div>
+
+
+        <div class="sidebar-toggle-group no-js">
+
+            <button class="sidebar-toggle" id="sidebar-hide" title="Hide the sidebar menu">
+                 «
+                <span class="show-for-small">hide menu</span>
+
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+            <button class="sidebar-toggle" id="sidebar-show" title="Show the sidebar menu">
+
+                <span class="show-for-small">menu</span>
+                <span class="hide-for-small">sidebar</span>
+                 »
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+
+      <div class="clearer"></div>
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+    <div class="relbar-bottom">
+
+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Nawigacja</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../../../genindex.html" title="Indeks ogólny"
+             >indeks</a></li>
+    <li><a href="../../../index.html">Matematyka  - dokumentacja</a> &#187;</li>
+
+        <li class="nav-item nav-item-this"><a href="">&lt;no title&gt;</a></li> 
+      </ul>
+    </div>
+    </div>
+
+    <div class="footer" role="contentinfo">
+    &#169; Copyright 2023, Maciej Sz.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 7.2.6.
+    </div>
+    <!-- cloud_sptheme 1.4 -->
+  </body>
+</html>
diff --git a/assets/notes/matematyka/matematyka_2023.11.20.html b/assets/notes/matematyka/matematyka_2023.11.20.html
@@ -81,7 +81,7 @@ <h1>Zadania<a class="headerlink" href="#zadania" title="Link to this heading">¶
 V'(x) = (a-2x)^2 -4x(a-2x) \\
 V'(x) = (a-2x)(a-2x -4x) \\
 V'(x) = (a-2x)(a-6x) \\
-x = \frac{a}{2} \or x = \frac{a}{6} \\
+x = \frac{a}{2} \lor x = \frac{a}{6} \\
 \end{split}\]</div>
 </div>
 <div class="admonition note">

diff --git a/assets/notes/matematyka/matematyka_2023.11.21.html b/assets/notes/matematyka/matematyka_2023.11.21.html
@@ -70,7 +70,7 @@ <h1>Sporządzanie wykresów funkcji<a class="headerlink" href="#sporzadzanie-wyk
 <li><p>faza I:</p>
 <ul>
 <li><p>“Dziedzina” funkcji</p></li>
-<li><p>granice na krańcach (e.g. w <span class="math notranslate nohighlight">\(\infty, -\inffty\)</span>)</p></li>
+<li><p>granice na krańcach (e.g. w <span class="math notranslate nohighlight">\(\infty, -\infty\)</span>)</p></li>
 <li><p>punkty charakterystyczne typu <span class="math notranslate nohighlight">\(f(0)\)</span></p></li>
 <li><p>szczególne własności funkcji (np. f jest parzysta <span class="math notranslate nohighlight">\(f(x) = f(-x)\)</span>)</p></li>
 <li><p>okresowość</p></li>

diff --git a/assets/notes/mechanika_cw/mechanika_cw_24.11.2023.html b/assets/notes/mechanika_cw/mechanika_cw_24.11.2023.html
@@ -0,0 +1,139 @@
+
+
+<!DOCTYPE html>
+
+<html lang="pl" data-content_root="../../../">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="viewport" content="width=device-width, initial-scale=1" />
+
+    <title>Mechanika - Ćwiczenia &#8212; Matematyka  - dokumentacja</title>
+    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/cloud.css?v=f9ae72be" />
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+    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=6897fae6" />
+    <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noticia+Text:400,i,b,bi|Open+Sans:400,i,b,bi|Roboto+Mono:400,i,b,bi&amp;display=swap" type="text/css" />
+
+    <script src="../../../_static/documentation_options.js?v=a28d12eb"></script>
+    <script src="../../../_static/doctools.js?v=888ff710"></script>
+    <script src="../../../_static/sphinx_highlight.js?v=dc90522c"></script>
+    <script src="../../../_static/translations.js?v=a186e9ce"></script>
+    <script src="../../../_static/sphinxcontrib-images/LightBox2/lightbox2/dist/js/lightbox-plus-jquery.min.js?v=ffc8af2d"></script>
+    <script src="../../../_static/sphinxcontrib-images/LightBox2/lightbox2-customize/jquery-noconflict.js?v=12818e64"></script>
+    <script>window.MathJax = {"options": {"processHtmlClass": "tex2jax_process|mathjax_process|math|output_area"}}</script>
+    <script defer="defer" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
+
+
+
+
+        <script src="../../../_static/jquery.cookie.js"></script>
+
+
+
+
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+
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+
+
+    <link rel="index" title="Indeks" href="../../../genindex.html" />
+    <link rel="search" title="Szukaj" href="../../../search.html" /> 
+        <meta name="viewport" content="width=device-width, initial-scale=1">
+  </head><body>
+    <div class="relbar-top">
+
+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Nawigacja</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../../../genindex.html" title="Indeks ogólny"
+             accesskey="I">indeks</a></li>
+    <li><a href="../../../index.html">Matematyka  - dokumentacja</a> &#187;</li>
+
+        <li class="nav-item nav-item-this"><a href="">Mechanika - Ćwiczenia</a></li> 
+      </ul>
+    </div>
+    </div>
+
+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+
+  <section class="tex2jax_ignore mathjax_ignore" id="mechanika-cwiczenia">
+<h1>Mechanika - Ćwiczenia<a class="headerlink" href="#mechanika-cwiczenia" title="Link to this heading">¶</a></h1>
+<p><strong>Siłą zachowawcza</strong> - praca siły na dowolnym zamkniętym torze jest równa 0</p>
+<div class="admonition-gradient admonition">
+<p class="admonition-title">Gradient</p>
+<div class="math notranslate nohighlight">
+\[
+grad F(x, y, z) = \vec{A}(x,y,z)
+(\frac{d}{dx}, \frac{d}{dy}, \frac{d}{dz})
+\]</div>
+</div>
+</section>
+
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper">
+<div id="searchbox" style="display: none" role="search">
+  <h3 id="searchlabel">Szybkie wyszukiwanie</h3>
+    <div class="searchformwrapper">
+    <form class="search" action="../../../search.html" method="get">
+      <input type="text" name="q" aria-labelledby="searchlabel" autocomplete="off" autocorrect="off" autocapitalize="off" spellcheck="false"/>
+      <input type="submit" value="Szukaj" />
+    </form>
+    </div>
+</div>
+<script>document.getElementById('searchbox').style.display = "block"</script>
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+                 »
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+
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+    <div class="relbar-bottom">
+
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+      <h3>Nawigacja</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../../../genindex.html" title="Indeks ogólny"
+             >indeks</a></li>
+    <li><a href="../../../index.html">Matematyka  - dokumentacja</a> &#187;</li>
+
+        <li class="nav-item nav-item-this"><a href="">Mechanika - Ćwiczenia</a></li> 
+      </ul>
+    </div>
+    </div>
+
+    <div class="footer" role="contentinfo">
+    &#169; Copyright 2023, Maciej Sz.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 7.2.6.
+    </div>
+    <!-- cloud_sptheme 1.4 -->
+  </body>
+</html>
diff --git a/index.html b/index.html
@@ -145,6 +145,7 @@ <h1>Wstęp<a class="headerlink" href="#wstep" title="Link to this heading">¶</a
 </li>
 </ul>
 </li>
+<li class="toctree-l1"><a class="reference internal" href="assets/index.html#mechanika-cwiczenia">Mechanika - Ćwiczenia</a></li>
 </ul>
 </div>
 <div class="admonition important">

diff --git a/objects.inv b/objects.inv
diff --git a/searchindex.js b/searchindex.js
-Original file line number
+Diff line change
@@ Expand Up @@
     </li>
     </ul>
     </li>
+    <li class="toctree-l1"><a class="reference internal" href="assets/index.html#mechanika-cwiczenia">Mechanika - Ćwiczenia</a></li>
     </ul>
     </div>
     <div class="admonition important">
@@ Expand Down @@