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How do I create the following rectangular symbol?

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I am interested in creating a symbol-sized tikz drawing with a rectangle half the width of the symbol (and the height of a symbol) and an arrow coming out from the middle right side of the rectangle pointing to the right (the arrow head should be rather small). I tried to do something like that here (the A symbol is for comparison in size), but it didn't quite work right:

\documentclass{article}  \usepackage{tikz}  \usetikzlibrary{positioning}  \begin{document}  \begin{tikzpicture}[   node distance = 0mm, box/.style = {% definition of rectangle as node     draw, line width=0.35mm,   text width=11pt, minimum height=11pt, align=left,   inner sep=1mm, outer sep=0pt}                     ] \node (box1) [label=above:{}] {}; \node (B) [draw, right=of box1] {}; \draw [->] (box1) -- (B);  \end{tikzpicture}  A  \end{document} 
  1. How do I make the width of the square half its size?
  2. How do I make the arrow leave the right side of the rectangle?
  3. How do I make an "empty" node to the right of the rectangle so I can draw an arrow to it?
  4. How do I make the arrow head smaller?

How do I create the following rectangular symbol?

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