Here are the examples.
#This file was created by <seak> Wed Nov 24 12:47:35 1999
#LyX 1.0 (C) 1995-1999 Matthias Ettrich and the LyX Team
\lyxformat 2.15
\textclass article
\language default
\inputencoding default
\fontscheme default
\graphics default
\paperfontsize default
\spacing single
\papersize Default
\paperpackage a4
\use_geometry 0
\use_amsmath 0
\paperorientation portrait
\secnumdepth 3
\tocdepth 3
\paragraph_separation indent
\defskip medskip
\quotes_language english
\quotes_times 2
\papercolumns 1
\papersides 1
\paperpagestyle default
\layout Standard
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\begin_inset Formula \( \sqrt{x^{2}+y^{2}} \)
\end_inset
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\the_end
#This file was created by <seak> Tue Nov 23 17:01:37 1999
#LyX 1.0 (C) 1995-1999 Matthias Ettrich and the LyX Team
\lyxformat 2.15
\textclass article
\language default
\inputencoding default
\fontscheme default
\graphics default
\paperfontsize default
\spacing single
\papersize Default
\paperpackage a4
\use_geometry 0
\use_amsmath 0
\paperorientation portrait
\secnumdepth 3
\tocdepth 3
\paragraph_separation indent
\defskip medskip
\quotes_language english
\quotes_times 2
\papercolumns 1
\papersides 1
\paperpagestyle default
\layout Standard
\begin_inset Formula \( \begin{array}{c}
\overrightarrow{t}=a_{11}\hat{x}+a_{12}\hat{y}\\
\overrightarrow{n}=a_{21}\hat{x}+a_{22}\hat{y}
\end{array} \)
\end_inset
\begin_inset Formula \( \Leftrightarrow \)
\end_inset
\begin_inset Formula \( \begin{array}{ll}
\displaystyle a_{11}=1, & a_{12}=\frac{x_{0}}{a_{0}}\\
a_{21}=-\frac{x_{0}}{a_{0}}, & a_{22}=1
\end{array} \)
\end_inset
\the_end
